
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 section of a railroad embankment is being constructed with a length of 100 meters. The cross-section of this embankment is an isosceles trapezoid with a lower base of 5 meters, an upper base of no less than 2 meters, and a slope angle of $45^{\circ}$. What height $h$ should this embankment be in order for the volume of earthworks to be no less than 400 cubic meters and no more than 500 cubic meters?

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