
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 wants to pass through a parabolic tunnel. The width at the arch (vertex) of the tunnel exactly spans a focal width of the parabola (a line segment perpendicular to the axis of symmetry of the parabola that intersects it at two points, denoted as \( p_1 \) and \( p_2 \)). To ensure that this truck can pass through the tunnel, what is the minimum width (at the base) the archway should be?

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