
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 $P(2, 1)$ with an inclination angle of $135^\circ$, establish a polar coordinate system with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis (the unit length is consistent with that of the rectangular coordinate system $xoy$). The equation of circle $C$ is $\rho = 4\cos\theta$.

1. Write the rectangular coordinate equation of circle $C$ and the parametric equation of line $l$.
2. Suppose circle $C$ intersects with line $l$ at points $A$ and $B$. Calculate $|PA| + |PB|$.

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