
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 the pole coincides with the origin of the Cartesian coordinate system and the polar axis aligns with the positive half of the x-axis, the polar equation of circle C is $\rho=4\cos \theta$. The parametric equation of line l is $\begin{cases} x=- \dfrac{3}{5}t+2 \\ y= \dfrac{4}{5}t+1 \end{cases}$ (where \(t\) is the parameter).
(1) Find the Cartesian coordinate equations for line l and circle C;
(2) Let point P(2,1), line l intersects circle C at points A and B, find the value of $|PA|\cdot|PB|$.

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