
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
From a circular log with radius \( R \), it is required to cut out a rectangular beam of maximum strength. It is known that the strength of the beam is directly proportional to the product of its width and the square of its height. What should the dimensions of the beam be to maximize its strength?

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