
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 a circle $C$ with center $\left(a,0\right)$ is tangent to a line with a slope of ${\frac{5π}{6}}$ at the point $N(3,-\sqrt{3})$, the equation of circle $C$ is ____.

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