## Step 1: Define the symbolic representation of the problem

The problem involves finding the best mix of two promotion packages, X and Y, to maximize profit. Let's define the symbolic variables:
- $x_1$ represents the number of packages X
- $x_2$ represents the number of packages Y

The objective function to maximize profit is: $70x_1 + 120x_2$

The constraints based on the availability of green and black tea are:
- $5x_1 + 3x_2 \leq 1200$ (green tea constraint)
- $2x_1 + 4x_2 \leq 900$ (black tea constraint)
- $x_1 \geq 0$ and $x_2 \geq 0$ (non-negativity constraints)

## Step 2: Express the problem in the required symbolic format

```json
{
    'sym_variables': [('x1', 'packages X'), ('x2', 'packages Y')],
    'objective_function': '70*x1 + 120*x2',
    'constraints': [
        '5*x1 + 3*x2 <= 1200',
        '2*x1 + 4*x2 <= 900',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Step 3: Translate the symbolic representation into Gurobi code

To solve this linear programming problem using Gurobi, we will use the Gurobi Python API.

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(lb=0, name="packages_X")
    x2 = model.addVar(lb=0, name="packages_Y")

    # Define the objective function
    model.setObjective(70*x1 + 120*x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(5*x1 + 3*x2 <= 1200, name="green_tea_constraint")
    model.addConstr(2*x1 + 4*x2 <= 900, name="black_tea_constraint")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Packages X: {x1.varValue}")
        print(f"Packages Y: {x2.varValue}")
        print(f"Maximum profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_tea_shop_problem()
```