
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
(1) Given in the Cartesian coordinate system, line $l$ passes through point $P(1,1)$ with an inclination angle of $\alpha= \frac{\pi}{6}$. Write the parametric equation of line $l$.  
(2) In the polar coordinate system, given the circle $\rho=10\cos\left(\frac{\pi}{3}-\theta\right)$, convert it into a Cartesian coordinate equation.

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