
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 $y^2 = 2px$ ($p > 0$), where $F$ is a focus, find $\tan \angle AMF$, where $l$ is a line passing through $F$ with a slope of $2$, intersecting the parabola at points $A$ and $B$, and $M$ is at $\left(-\frac{p}{2}, 0\right)$.

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