
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 Cartesian coordinate system, the curve defined by $\begin{cases} x=2\cos a+2 \\ y=\sin a \end{cases}$ (where $a$ is a parameter) is transformed into curve $C_1$ by keeping the $x$-coordinate of each point unchanged and doubling the $y$-coordinate. In the polar coordinate system established with the origin as the pole and the non-negative half-axis of $x$ as the polar axis, the equation of curve $C_2$ is $p=4\sin \theta$.
(I) Find the standard equations of $C_1$ and $C_2$.
(II) Find the polar equation of the perpendicular bisector of the common chord of $C_1$ and $C_2$.

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