
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, a circle $C$ has its center at $C(3, \frac{π}{6})$ and radius $r=1$. Point $Q$ moves on circle $C$.
(1) Find the polar coordinate equation of circle $C$;
(2) If point $P$ moves on line $OQ$ and $OQ$ : $QP = 2$ : $3$, find the trajectory equation of point $P$.

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