
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 square base of the pyramid \(ABCD\) has lateral faces that are equilateral triangles. The plane \(S\) passing through the edge \(AB\) divides the volume of the pyramid into two equal parts. What is the angle between plane \(S\) and the base of the pyramid?

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