## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'medical platoons' and 'signal platoons', which we can denote as $x_1$ and $x_2$ respectively. The objective function to maximize is $6x_1 + 7x_2$. The constraints are:
1. $1x_1 + 2x_2 \geq 12$ (deployment weight constraint)
2. $7x_1 - 10x_2 \geq 0$ (medical and signal platoons relationship constraint)
3. $1x_1 + 2x_2 \leq 25$ (combined deployment weight constraint)
4. $x_1, x_2$ are integers (whole number constraint)

## Step 2: Convert the problem into a symbolic representation
The symbolic representation of the variables is:
- $x_1$ for 'medical platoons'
- $x_2$ for 'signal platoons'

The objective function is: $6x_1 + 7x_2$

The constraints are:
1. $x_1 + 2x_2 \geq 12$
2. $7x_1 - 10x_2 \geq 0$
3. $x_1 + 2x_2 \leq 25$
4. $x_1, x_2 \geq 0$ and are integers.

## 3: Express the problem in the required JSON format
```json
{
'sym_variables': [('x1', 'medical platoons'), ('x2', 'signal platoons')],
'objective_function': '6*x1 + 7*x2',
'constraints': [
    'x1 + 2*x2 >= 12',
    '7*x1 - 10*x2 >= 0',
    'x1 + 2*x2 <= 25',
    'x1, x2 are integers and >= 0'
]
}
```

## 4: Implement the problem using Gurobi
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="medical_platoons", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="signal_platoons", vtype=gurobi.GRB.INTEGER)

    # Define the objective function
    model.setObjective(6 * x1 + 7 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(x1 + 2 * x2 >= 12, name="deployment_weight_min")
    model.addConstr(7 * x1 - 10 * x2 >= 0, name="medical_signal_relationship")
    model.addConstr(x1 + 2 * x2 <= 25, name="combined_deployment_weight_max")

    # Solve the model
    model.optimize()

    # Check if the model is optimized
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Medical platoons: {x1.varValue}")
        print(f"Signal platoons: {x2.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```