
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 $C$ with the parametric equations $x=2\cos \theta$ and $y=2\sin \theta$, and a line $l$ with the polar equation $\rho = \frac{4}{\sin \theta + \cos \theta}$ in a coordinate system where the origin is the pole and the positive $x$-axis is the polar axis. Let point $P$ be on line $l$.

(1) Find the minimum value of the distance $|PF|$, where $F$ is the point of tangency of the tangent line to circle $C$ passing through point $P$.

(2) Let ray $OP$ intersect circle $C$ at point $R$, and let point $Q$ be on ray $OP$ such that $|OP|^2 = |OQ| \cdot |OR|$. Find the polar equation of the locus of point $Q$.

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