
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 parametric equations of the curve $C_1$ are given by $\begin{cases} x=2\cos\theta \\ y=\sin\theta \end{cases}$ (where $\theta$ is the parameter). In the polar coordinate system established with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis, the polar equation of the curve $C_2$ is $\rho^2 = 4\rho\sin\theta - 3$.
(I) Write the rectangular coordinate equations for the curves $C_1$ and $C_2$;
(II) If $P$ and $Q$ are moving points on the curves $C_1$ and $C_2$, respectively, find the maximum value of $|PQ|$.

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