
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 sheet of metal shaped like an isosceles right triangle, we create a box with the same base and equal height side walls by cutting out the shaded areas. For what height will the volume of the box be maximized?

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