
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Determine the condition under which the roots of the quadratic equation $ax^2 + 4ax + c = 0$ are equal.
**A)** $c = a$  
**B)** $c = 2a$  
**C)** $c = 4a$  
**D)** $c = 3a$

Present the answer in LaTex format: \boxed{Your answer}
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