
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
Transform every point on the unit circle $x^2+y^2=1$ by doubling the x-coordinate and tripling the y-coordinate to obtain curve $\Gamma$.

(I) Write the parametric equations for $\Gamma$.
(II) Suppose the line $l: 3x+2y-6=0$ intersects $\Gamma$ at points $P_1$ and $P_2$. In a polar coordinate system with the origin as the pole and the positive x-axis as the polar axis, find the polar equation of the line that passes through the midpoint of segment $P_1P_2$ and is perpendicular to $l$.

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