
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 rectangular coordinate system, the line $l$ passes through the point $P(2,2)$ with an angle of inclination of $\alpha = \frac{\pi}{3}$. Establish a polar coordinate system with the origin of the rectangular coordinate system as the pole and the positive semi-axis of the $c > 0$ axis as the polar axis, using the same length unit for both systems. The polar equation of circle $C$ is $\rho = 2\cos\theta$.

(I) Write the parametric equation of line $l$ and the rectangular equation of circle $C$.

(II) Line $l$ intersects circle $C$ at points $A$ and $B$. Find the value of $\frac{1}{|PA|} + \frac{1}{|PB|}$.

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