
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 the distance from point $M(2,m)$ on the parabola $y^2=2px$ to the focus $F$ is $3$, and the angle of inclination of the line $l$ passing through focus $F$ is $60^\circ$.

(I) Find the equation of the parabola;

(II) Find the length of the chord cut off by the line $l$ on the parabola.

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