
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
In the polar coordinate system, it is known that the circle is defined by $\rho=10\cos\left(\frac{\pi}{3}-\theta\right)$.

(1) Find the equation of the circle in Cartesian coordinates.
(2) Let P be any point on the circle, find the maximum distance from point P to the line $\sqrt{3}x-y+2=0$.

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