
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 base of a pyramid is an equilateral triangle with a side length of 1. Out of the three vertex angles at the apex of the pyramid, two are right angles.

Find the maximum volume of the pyramid.

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