
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
Given the polar equation of curve $C_1$ is $\rho^2 - 4\rho\cos\theta - 4 = 0$, and curve $C_2$ is symmetric to curve $C_1$ with respect to the line $\theta = \frac{\pi}{4}$, find the polar equation of curve $C_2$.

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