
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
A truck that is 3 meters high and 1.6 meters wide needs to pass through a parabolic tunnel. The width of the tunnel's arch is exactly the length of the latus rectum of the parabola (a segment perpendicular to the parabola's axis of symmetry and intersecting the parabola at two points \(p_{1}\) and \(p_{2}\), known as the latus rectum). To ensure the truck can pass through the tunnel, what should be the minimum width of the arch?

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