
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 $O$ as the pole and the positive semi-axis of the $x$-axis as the polar axis, establish a polar coordinate system with the same unit length.
(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 $Q$ is on ray $OP$ and satisfies $|OQ|⋅|OP|=|OR|^{2}$. Find the polar coordinate equation of the trajectory of point $Q$ as point $P$ moves on line $l$.

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