
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 parabola $C$: ${y}^{2}=2px (p > 0)$ with focus $F$, latus rectum $l$: $x=-\frac{5}{4}$, point $M$ on parabola $C$, point $A$ on latus rectum $l$. If $MA \perp l$, and the angle of inclination of line $AF$ is $\frac{\pi}{3}$, then $|MF|=$ ________.

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