To solve the optimization problem described, we first need to convert the natural language description into a symbolic representation. Let's denote:

- $x_1$ as the number of coats sold,
- $x_2$ as the number of shirts sold.

The objective function aims to maximize profit. Given that a coat is sold for a profit of $12 and a shirt for a profit of $8, the objective function can be represented algebraically as:

$$
\text{Maximize: } 12x_1 + 8x_2
$$

The constraints are as follows:
1. The store can spend at most $50,000 on coats and shirts. Since a coat costs $55 and a shirt costs $25, this constraint is represented as:
   $$
   55x_1 + 25x_2 \leq 50000
   $$
2. At least 60 but at most 100 coats are sold each month:
   $$
   60 \leq x_1 \leq 100
   $$
3. The number of shirts sold is at most four times the number of coats sold:
   $$
   x_2 \leq 4x_1
   $$

The symbolic representation in JSON format, as requested, would be:

```json
{
    'sym_variables': [('x1', 'number of coats sold'), ('x2', 'number of shirts sold')],
    'objective_function': '12*x1 + 8*x2',
    'constraints': [
        '55*x1 + 25*x2 <= 50000',
        '60 <= x1 <= 100',
        'x2 <= 4*x1'
    ]
}
```

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

```python
from gurobipy import *

# Create a new model
m = Model("Clothing_Store_Optimization")

# Define variables
x1 = m.addVar(name='coats_sold', lb=60, ub=100, vtype=GRB.INTEGER)
x2 = m.addVar(name='shirts_sold', lb=0, vtype=GRB.INTEGER)

# Objective function: Maximize profit
m.setObjective(12*x1 + 8*x2, GRB.MAXIMIZE)

# Constraints
m.addConstr(55*x1 + 25*x2 <= 50000, name='budget_constraint')
m.addConstr(x2 <= 4*x1, name='shirts_vs_coats')

# Optimize the model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Coats sold: {x1.x}")
    print(f"Shirts sold: {x2.x}")
    print(f"Maximum profit: ${12*x1.x + 8*x2.x:.2f}")
else:
    print("No optimal solution found")

```