
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
Coordinate Systems and Parametric Equations (Elective 4-4):

In the rectangular coordinate system $xOy$, the parametric equations of curve $C_1$ are given by $\begin{cases} x=2-\frac{3}{5}t \\ y=-2+\frac{4}{5}t \end{cases}$ ($t$ is the parameter). By establishing a polar coordinate system with the coordinate origin as the pole and the positive half of the $x$-axis as the polar axis, the polar equation of curve $C_2$ is given by $\rho \cos \theta = \tan \theta$.

(1) Find the Cartesian equation of curve $C_1$ and the rectangular coordinate equation of curve $C_2$.
(2) If curves $C_1$ and $C_2$ intersect at points $A$ and $B$, and the polar coordinates of point $P$ are $(2\sqrt{2}, -\frac{\pi}{4})$, find the value of $\frac{1}{|PA|} + \frac{1}{|PB|}$.

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