
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
In the polar coordinate system, $O$ is the pole, and the center of circle $C$ is $(1, \frac{3\pi}{4})$, with radius $r=1$. Point $P$ moves on circle $C$.
(I) Find the polar coordinate equation of circle $C$;
(II) Establish a rectangular coordinate system with the pole $O$ as the origin and the positive semi-axis of the $x$-axis as the polar axis. The coordinates of point $A$ are $(1, 0)$, and $Q$ is the midpoint of segment $AP$. Find the rectangular coordinate equation of the trajectory of point $Q$.

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