
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 $\tan \alpha=-2$, the focus of the parabola $y^{2}=2px (p > 0)$ is $F(-\sin \alpha\cos \alpha,0)$, and line $l$ passes through point $F$ and intersects the parabola at points $A$ and $B$ with $|AB|=4$, find the distance from the midpoint of segment $AB$ to the line $x=-\frac{1}{2}$.

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