
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 parametric equations of curve $({C}_{1})$ are given by $x=2-\frac{3}{5}t,y=-2+\frac{4}{5}t$ ($t$ is the parameter), and in the polar coordinate system with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis, the polar equation of curve $({C}_{2})$ is given by $\rho \cos \theta =\tan \theta$.

(1) Find the ordinary equation of curve $({C}_{1})$ and the rectangular coordinate equation of curve $({C}_{2})$;
(2) If curve $({C}_{1})$ intersects curve $({C}_{2})$ at points $A$ and $B$, and the polar coordinates of point $P$ are $(2\sqrt{2},-\frac{\pi }{4})$, find the value of $|PA|\cdot |PB|$.

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