<Question>
The average of Amy's, Ben's, and Chris's ages is 6. Four years ago,  Chris was the same age as Amy is now. In four years, Ben's age will be $\frac{3}{5}$ of Amy's age at that time. How many years old is Chris now?
</Question>

<think>
<Plan_1>
Okay, let's see. I need to figure out how old Chris is now based on the given information. Hmm, let's break down the problem step by step. First, the problem mentions three people: Amy, Ben, and Chris. Their ages are related through some average, past, and future ages. Let me parse each piece of information carefully.

The first piece of information is that the average of their ages is 6. Since there are three people, the average age being 6 means that the total sum of their ages is 6 times 3, which is 18.
So, Amy + Ben + Chris = 18. Let me note that down as equation (1):
A + B + C = 18

Next, the problem states, "Four years ago, Chris was the same age as Amy is now." So, four years ago, Chris's age was equal to Amy's current age. Let me translate that into an equation.

<prompt_1.1> Translate the statement "Four years ago, Chris was the same age as Amy is now" into an equation. </prompt_1.1>

Then, the third piece of information is: "In four years, Ben's age will be 3/5 of Amy's age at that time." So, in four years, Ben's age (B + 4) will be equal to 3/5 of Amy's age at that time (which is A + 4). Let me write that as equation (3):
B + 4 = (3/5)(A + 4)

Now, the question is asking for Chris's current age, which is C. So, we need to solve for C. Let's see how we can use these three equations to find C.

First, from equation (1), we have A + B + C = 18. If we can express A and B in terms of C, or find another relation, maybe we can substitute into this equation.

<prompt_1.2> Plan how to solve the system of equations to find Chris's current age. </prompt_1.2>
</Plan_1>

<Execution_1>
<execution_1.1>
If Chris's current age is C, then four years ago, her age was C - 4. According to the problem, this is equal to Amy's current age. So:

C - 4 = A
</execution_1.1>

<execution_1.2>
Let's look at equation (2): C - 4 = A. So, Amy's age is Chris's age minus 4. That means A = C - 4. That's helpful. So, we can substitute A in terms of C into the other equations.

Similarly, equation (3) relates B and A. Since we can express A in terms of C, perhaps we can also express B in terms of C. Let's try that.
</execution_1.2>
</Execution_1>

<Plan_2>
Based on execution_1.1, execution_1.2:
From equation (2): A = C - 4. Let's substitute this into equation (3):
B + 4 = (3/5)(A + 4)  
But A is C - 4, so substitute that in:
B + 4 = (3/5)( (C - 4) + 4 )  
Simplify inside the parentheses: (C - 4 + 4) = C. So:

B + 4 = (3/5)(C)  
Therefore, B = (3/5)C - 4

Wait, let me check that again. If (C - 4) + 4 is indeed C, so then yes, the equation becomes B + 4 = (3/5)C. Then subtract 4 from both sides: B = (3/5)C - 4.
Hmm, that seems correct.

Now, we can substitute both A and B in terms of C into equation (1). Let's do that.
Equation (1): A + B + C = 18  
Substitute A = C - 4 and B = (3/5)C - 4:

<prompt_2.1> Substitute A and B in terms of C into equation (1) and solve for C. </prompt_2.1>
</Plan_2>

<Execution_2>
<execution_2.1>
(C - 4) + [(3/5)C - 4] + C = 18

Combine like terms:

C - 4 + (3/5)C - 4 + C = 18

First, combine the C terms: C + (3/5)C + C. Let's compute that:

C is 1C, so 1C + (3/5)C + 1C = (1 + 3/5 + 1)C = (2 + 3/5)C = (13/5)C

Then, the constants: -4 -4 = -8

So, the equation becomes:

(13/5)C - 8 = 18

Now, solve for C:

Add 8 to both sides:

(13/5)C = 26

Multiply both sides by 5/13:

C = 26 * (5/13)

Simplify:

26 divided by 13 is 2, so 2 * 5 = 10

So, C = 10.
</execution_2.1>
</Execution_2>

<Plan_3>
Based on execution_2.1:
Wait, so Chris is 10 years old now? Let me verify this because that seems straightforward, but let's check if all the conditions are satisfied.

<prompt_3.1> Verify the solution by checking if all conditions are satisfied with Chris's age of 10. </prompt_3.1>

But let me check again my equations to make sure I didn't make any mistakes in substitution.

Starting again:

<prompt_3.2> Recheck the equations and verify the solution for Chris's age. </prompt_3.2>

But wait, let me check the third condition again. In four years, Ben's age will be 3/5 of Amy's age. Let's compute Ben's age in four years: 6 + 4 = 10.

<prompt_3.3> Recheck the third condition and confirm the solution. </prompt_3.3>

Hmm, but let me think again. Is there another way this could be interpreted? For example, when the problem says "Four years ago, Chris was the same age as Amy is now," does that mean Chris's age four years ago equals Amy's current age? Yes, that's how I interpreted it.
So, C - 4 = A. Which leads to A = C - 4. That seems correct.

Another possible source of error could be in the third condition. Let me parse that again: "In four years, Ben's age will be 3/5 of Amy's age at that time". So, in four years, Ben's age is B + 4, and Amy's age at that time will be A + 4. So, B + 4 = (3/5)(A + 4). That's how I set it up, which seems correct.

Another check: Let's verify all the ages.

<prompt_3.4> Perform a final verification of all conditions and conclude the solution. </prompt_3.4>
</Plan_3>

<Execution_3>
<execution_3.1>
First, check the average age: Amy is 6, Ben is 6, Chris is 10. The sum is 6 + 6 + 10 = 22. Wait, that's not 18. Wait, that can't be right. There's a mistake here.
</execution_3.1>

<execution_3.2>
Ages:

Amy (A) = C - 4 = 10 - 4 = 6. So Amy is 6 now.

Ben (B) = (3/5)C - 4 = (3/5)*10 - 4 = 6 - 4 = 2. So Ben is 2 now.

Chris (C) = 10.

Check the sum: 6 + 2 + 10 = 18. Correct, which matches equation (1).

Now check the other conditions:

Four years ago, Chris was 10 - 4 = 6. Amy's current age is 6. So that matches the second condition.

In four years, Ben will be 2 + 4 = 6. Amy will be 6 + 4 = 10. 3/5 of Amy's age at that time is (3/5)*10 = 6. So Ben's age in four years is 6, which is 3/5 of Amy's age then. That matches the third condition.
</execution_3.2>

<execution_3.3>
Amy's age in four years will be 4 + 4 = 8? Wait, Amy is currently 4. So in four years, she'll be 4 + 4 = 8. Then 3/5 of Amy's age then is (3/5)*8 = 24/5 = 4.8. But according to the equation, Ben's current age is 6. So in four years, Ben will be 6 + 4 = 10. But 10 is supposed to be equal to 4.8? That's not possible.
</execution_3.3>

<execution_3.4>
If Chris is 10 now, then four years ago he was 10 - 4 = 6. Amy's current age is 6. So, Amy is 6 now. Then Ben's age is 18 - 10 - 6 = 2. So, Ben is 2 years old now.

In four years, Ben will be 6, and Amy will be 10. So, 3/5 of Amy's age at that time would be (3/5)*10 = 6. So, Ben's age in four years is 6, which is equal to 3/5 of Amy's age then. That checks out.

Another check: The average age is (6 + 2 + 10)/3 = 18/3 = 6. Correct.

Four years ago, Chris was 6, which is equal to Amy's current age. Correct.

So, all conditions are satisfied.
</execution_3.4>
</Execution_3>

<Final_answer>
Therefore, based on the calculations above, Chris is currently $\boxed{10}$ years old.
</Final_answer>
</think>