
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 an inclination angle of $\frac{2\pi}{3}$, and the polar coordinate equation of a circle is $\rho = 2\cos\left(\theta + \frac{\pi}{3}\right)$.

(1) Find the parametric equation of line $l$ and the general form equation of the circle.

(2) Suppose line $l$ intersects 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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