
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 circle $C$: $x^{2}+y^{2}=4$, line $l$: $x+y=2$, with the origin $O$ as the pole and the positive semi-axis of the $x$-axis as the polar axis, establish a polar coordinate system.
(1) Convert the equations of circle $C$ and line $l$ into polar coordinate equations.
(2) Point $P$ is on line $l$, and ray $OP$ intersects circle $C$ at point $R$. Point $Q$ lies on $OP$ and satisfies $|OQ| \cdot |OP| = |OR|^{2}$. Determine the polar coordinate equation of the locus of point $Q$.

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