
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
(5 points) A line passing through the focus of the parabola $y^2=4x$ intersects the parabola at points A$(x_1, y_1)$ and B$(x_2, y_2)$. If $x_1+x_2=6$, then $|AB|=$　.

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