
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 polar coordinate equation of a circle as $ρ=4\cos θ$, the center of the circle as $C$, and the polar coordinates of point $P$ as $\left(4,\frac{π}{3}\right)$, determine the value of $|CP|$.

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