
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 the curve $C_1$ with the polar coordinate equation: $\rho =4\cos \theta $, and curve $C_2$ with the parametric equations: $$\begin{cases}x=3- \frac{1}{2}t \\ y= \frac{ \sqrt{3}}{2}t\end{cases} (t \text{ is the parameter }),$$ and point $A(3,0)$.

(1) Find the rectangular coordinate equation for curve $C_1$ and the general form equation for curve $C_2$.

(2) Suppose curves $C_1$ and $C_2$ intersect at points $P$ and $Q$. Find the value of $|AP|\bullet |AQ|$.

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