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

Let's denote the number of plush toys as $x_1$ and the number of action figures as $x_2$. The objective is to maximize profit, which is $4x_1 + 4.50x_2$. The constraints are based on the available time for assembly and packaging.

## Step 2: Formulate the objective function and constraints

- Objective function: Maximize $4x_1 + 4.50x_2$
- Constraints:
  - Assembly time: $20x_1 + 15x_2 \leq 1200$
  - Packaging time: $4x_1 + 5x_2 \leq 900$
  - Non-negativity: $x_1 \geq 0, x_2 \geq 0$

## 3: Symbolic representation in the required format

```json
{
    'sym_variables': [('x1', 'plush toys'), ('x2', 'action figures')],
    'objective_function': '4*x1 + 4.50*x2',
    'constraints': [
        '20*x1 + 15*x2 <= 1200',
        '4*x1 + 5*x2 <= 900',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## 4: Convert the problem into Gurobi code

To solve this problem using Gurobi in Python, we will use the following code:

```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name="plush_toys", lb=0, ub=None, obj=4)
    x2 = model.addVar(name="action_figures", lb=0, ub=None, obj=4.50)

    # Add constraints
    model.addConstr(20*x1 + 15*x2 <= 1200, name="assembly_time")
    model.addConstr(4*x1 + 5*x2 <= 900, name="packaging_time")

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

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Number of plush toys: {x1.x}")
        print(f"Number of action figures: {x2.x}")
        print(f"Max Profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_toy_shop_problem()
```

The provided Gurobi code defines the variables, sets up the objective function and constraints, and solves the optimization problem to determine the optimal number of plush toys and action figures to maximize profit.