
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 $(xOy)$, the equation of curve $(C_{1})$ is $\frac{x^{2}}{9}+y^{2}=1$. Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis. The polar coordinate equation of curve $(C_{2})$ is $\rho^{2}-8\rho\sin \theta+15=0$.
(I) Write the parametric equation of $(C_{1})$ and the rectangular coordinate equation of $(C_{2})$;
(II) If point $P$ is on $(C_{1})$ and point $Q$ is on $(C_{2})$, find the maximum value of $|PQ|$.

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