
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 two-dimensional rectangular coordinate system, establish a polar coordinate system with the coordinate origin as the pole and the non-negative semi-axis of the $x$-axis as the polar axis. The polar coordinate equation of the curve $C$ is given by: $\rho=4\cos \theta$, and the parametric equation of the line $l$ is given by: $ \begin{cases} x=3+ \frac{\sqrt{3}}{2}t \\ y=\frac{1}{2}t \end{cases} (t \text{ is the parameter}) $. The line $l$ intersects the curve $C$ at points $P_{1}$ and $P_{2}$.

(1) Find the rectangular coordinate equation of the curve $C$ and the general form equation of the line $l$.
(2) Given $Q(3,0)$, find the value of $||P_{1}Q|-|P_{2}Q||$.

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