
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 line $l$ passes through point $P(-1,2)$ with a slope angle of $\frac{2\pi}{3}$, and the circle's equation is $\rho=2\cos (\theta+\frac{\pi}{3})$:
(1) Find the parametric equation of line $l$;
(2) Let line $l$ intersect the circle at points $M$ and $N$, find the value of $|PM|\cdot|PN|$.

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