
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 line $\begin{cases} x=1+t\cos\alpha \\ y=t\sin\alpha \end{cases}$ (where $t$ is a parameter) intersects with the parabola $y^2=4x$ at points A and B. If the coordinates of the midpoint of line segment AB are $(m, 2)$, the length of line segment AB is _____.

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