
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
Given square ABCD is folded along the diagonal AC, determine the angle formed by line BD and plane ABC when the volume of the regular pyramid with vertices A, B, C, and D is maximized.

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