
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 rectangular coordinate system $(xOy)$, establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis. The curves $({C}_{1})$: $ρ =4\cos θ (0≤θ < \frac{π }{2})$ and $({C}_{2})$: $ρ \cos θ =3$.

(1) Find the polar coordinates of the intersection point(s) of $({C}_{1})$ and $({C}_{2})$;
(2) Given point $Q$ on $({C}_{1})$ with $\overrightarrow{OQ}=\frac{2}{3}\overrightarrow{QP}$, find the polar coordinate equation of the moving point $P$.

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