
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
The bending resistance of a beam with a rectangular cross-section is proportional to the product of its width and the square of its height. What should be the width of the beam section, cut from a round log with a diameter of \( 15 \sqrt{3} \), to maximize its bending resistance?

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