
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 that curve $C$ is symmetric with respect to the polar axis of the curve $\rho=5 \sqrt{3}\cos -5\sin \theta$, determine the equation of curve $C$.

A) $\rho=-10\cos \left(\theta- \dfrac{\pi}{6}\right) $
B) $\rho=10\cos \left(\theta- \dfrac{\pi}{6}\right) $
C) $\rho=-10\cos \left(\theta+ \dfrac{\pi}{6}\right) $
D) $\rho=10\cos \left(\theta+ \dfrac{\pi}{6}\right) $

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