
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 a parabola $y^{2}=2px$ with a point $M(2,m)$ on it, the distance from $M$ to the focus $F$ is $3$. The line $l$ passes through the focus $F$ and has an inclination angle of $60^{\circ}$.
$(1)$ Find the equation of the parabola;
$(2)$ Find the length of the chord intercepted on the parabola by the line $l$.

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