
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 the line $l$: $\begin{cases} x=a+m\cdot \sin \theta \\ y=b+m\cdot \cos \theta \end{cases}(m$ is a parameter$)$

(1) When $\theta = \frac{\pi}{3}$, find the slope of the line $l$;

(2) If $P(a,b)$ is a point inside the circle $O$: $x^{2}+y^{2}=4$, and $l$ intersects the circle $O$ at points $A$ and $B$, such that $|PA|$, $|OP|$, and $|PB|$ form a geometric sequence, find the trajectory equation of the moving point $P$.

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