
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
Given a circle $x^{2}+y^{2}=1$, each point on the circle has its x-coordinate remain unchanged while its y-coordinate becomes twice the original value, resulting in a curve $C$. Establish a polar coordinate system with the coordinate origin as the pole and the positive half of the x-axis as the polar axis. The polar coordinate equation of line $l$ is $2ρ\cos θ+ρ\sin θ-2=0$.
(1) Write the parametric equation of $C$ and the rectangular coordinate equation of line $l$.
(2) Denote the intersection points of line $l$ and curve $C$ as $P_{1}$ and $P_{2}$. Determine the polar coordinate equation of the line passing through the midpoint of segment $P_{1}P_{2}$ and perpendicular to $l$.

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