
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 rectangular coordinate system $xOy$, the equation of the parabola $C$ is $y^2=2px$ $(p>0)$, with point $O$ as the focus and the positive semi-axis of $x$ as the polar axis. Establish a polar coordinate system, and the polar coordinate equation of the line $l$ is $2ρ\sin(θ-\frac{π}{3})=\sqrt{3}$, intersecting the $x$-axis at point $M$.
(1) Find the rectangular coordinate equation of $l$ and the polar coordinates of point $M$;
(2) Suppose line $l$ intersects parabola $C$ at points $A$ and $B$, and the distances $|MA|$, $|AB|$, and $|MB|$ form a geometric sequence. Find the value of $p$.

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