
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
All edges of a regular quadrilateral pyramid \(S A B C D\) with base \(A B C D\) are of equal length. Plane \(\alpha\) is perpendicular to line \(S A\), and plane \(\beta\) is parallel to line \(C D\). Determine the smallest possible angle between planes \(\alpha\) and \(\beta\).

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