
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 a line $l$ passing through point $P(-1,2)$ and with a slope angle of $\frac{2\pi}{3}$, and a circle equation given by $\rho=2\cos\left(\theta+ \frac{\pi}{3}\right)$:
1. Find the parametric equation of line $l$;
2. Let's say line $l$ intersects with 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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