
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
Consider a tunnel designed as a four-lane, two-way road with a total lane width of 22 meters and a vehicle height limit of 4.5 meters. The total length of the tunnel is 25 kilometers, and the tunnel's archway can be approximated as half of an elliptical shape.

1. If the maximum arch height \( h \) is 6 meters, what is the width \( l \) of the tunnel's arch?
2. If the maximum arch height \( h \) is no less than 6 meters, how should the arch height \( h \) and arch width \( l \) be designed to minimize the volume of earthwork for the tunnel? (The area of a half-ellipse is given by \( S = \frac{\pi}{4} l h \), and the volume of a cylinder is given by the base area multiplied by the height. All results should be accurate to 0.1 meters.)

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