
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 $C$ with the polar coordinate equation $ρ=4\cos θ$, a Cartesian coordinate system is established with the pole as the origin and the positive half of the polar axis as the $x$-axis. The parameter equation of line $L$ is given by $ \begin{cases} x=5+ \frac { \sqrt {3}}{2}t \\ y= \frac {1}{2}t \end{cases}(t \text{ is the parameter}) $.

(1) Find the Cartesian coordinate equation of the curve $C$ and the general equation of the line $L$.

(2) If the curve $C$ intersects with the line $L$ at points $P$ and $Q$, find $|PQ|$.

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