
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
(Optional Course 4-4: Coordinate Systems and Parametric Equations)
Given that line $l$ passes through point $P(-1,2)$ with an angle of inclination of $\frac{2π}{3}$, and the equation of a circle is given by $p=2\cos\left(θ+\frac{π}{3}\right)$.
(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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