## Step 1: Define the symbolic representation of the problem
Let's denote the number of large coffees as $x_1$ and the number of small coffees as $x_2$. The objective is to maximize profit, where the profit per large coffee is $5 and per small coffee is $3. Therefore, the objective function can be represented as $5x_1 + 3x_2$.

## Step 2: Identify the constraints based on the given resources
The shop has 1000 units of coffee beans and 1500 units of milk available. A large coffee takes 12 units of coffee beans and 20 units of milk, while a small coffee takes 8 units of coffee beans and 15 units of milk. This gives us two constraints:
1. $12x_1 + 8x_2 \leq 1000$ (coffee beans constraint)
2. $20x_1 + 15x_2 \leq 1500$ (milk constraint)
Additionally, $x_1 \geq 0$ and $x_2 \geq 0$ because the number of coffees cannot be negative.

## 3: Express the problem in the required symbolic format
The symbolic variables are:
- $x_1$ for large coffees
- $x_2$ for small coffees

The objective function is: $5x_1 + 3x_2$

The constraints are:
- $12x_1 + 8x_2 \leq 1000$
- $20x_1 + 15x_2 \leq 1500$
- $x_1 \geq 0$
- $x_2 \geq 0$

In the required format:
```json
{
'sym_variables': [('x1', 'large coffees'), ('x2', 'small coffees')],
'objective_function': '5*x1 + 3*x2',
'constraints': [
    '12*x1 + 8*x2 <= 1000',
    '20*x1 + 15*x2 <= 1500',
    'x1 >= 0',
    'x2 >= 0'
]
}
```

## 4: Translate the problem into Gurobi code
```python
import gurobi

def solve_coffee_shop_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name="large_coffees", lb=0, ub=gurobi.GRB.INFINITY)
    x2 = model.addVar(name="small_coffees", lb=0, ub=gurobi.GRB.INFINITY)

    # Set the objective function
    model.setObjective(5 * x1 + 3 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(12 * x1 + 8 * x2 <= 1000, name="coffee_beans_constraint")
    model.addConstr(20 * x1 + 15 * x2 <= 1500, name="milk_constraint")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: large coffees = {x1.varValue}, small coffees = {x2.varValue}")
        print(f"Maximum profit: ${5 * x1.varValue + 3 * x2.varValue:.2f}")
    else:
        print("No optimal solution found")

solve_coffee_shop_problem()
```