
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
At the base of the pyramid \(S A_{1} A_{2} \ldots A_{n}\) lies point \(O\), and it is given that \(S A_{1}=S A_{2}=\ldots=S A_{n}\) and \(\angle S A_{1} O = \angle S A_{2} O = \ldots = \angle S A_{n} O\).

For what smallest value of \(n\) does it follow that \(SO\) is the height of the pyramid?

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