
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
In the Cartesian coordinate system $xOy$, there is a circle C: $(x-1)^2 + y^2 = 1$, a line $l_1$: $y = \sqrt{3}x$, and a line $l_2$ passing through point P(2, -1) with an inclination angle of $\frac{2π}{3}$. Establish a polar coordinate system with the origin O as the pole and the positive semi-axis of the x-axis as the polar axis.

1. Write the polar coordinates of the intersection points of line $l_1$ and circle C, as well as the parametric equations of line $l_2$.
2. If line $l_2$ intersects with circle C at points E and F, find the value of $|PE| \cdot |PF|$.

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