
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 $xOy$, the curve $C$ is defined by the parametric equations: $$C: \begin{cases} x = 1 + 2\cos\alpha \\ y = -1 + 2\sin\alpha \end{cases}$$, where $\alpha$ is a parameter. With the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis, establish a polar coordinate system. The polar coordinate equation of the line $l$ is given by: $$\rho\cos(\theta + \frac{\pi}{4}) = \frac{\sqrt{2}}{2}$$.
(1) Find the ordinary equation of the curve $C$ and the rectangular coordinate equation of the line $l$;
(2) If the curve $C$ intersects the line $l$ at points $A$ and $B$, and point $P$ is $(1, 0)$, find the value of: $$\frac{|PA|}{|PB|} + \frac{|PB|}{|PA|}$$.

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