
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 that P is a point on the semicircle C: $$\begin{cases} \overset{x=\cos\theta }{y=\sin\theta }\end{cases}$$ (where $\theta$ is the parameter, $0\leq\theta\leq\pi$), the coordinates of point A are (1, 0), O is the origin, and point M is on the ray OP. The length of segment OM and the arc $$\hat{AP}$$ of C are both $$\frac{\pi}{3}$$.  
(1) Establish a polar coordinate system with O as the pole and the positive x-axis as the polar axis, and find the polar coordinates of point M;  
(2) Find the parametric equation of the line AM.

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