
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 an integer \(n\) such that \(n \geq 2\), let \(A\) be a set of positive integers where the smallest element is 1 and the largest element is \(a\), such that \(7 \times 3^{n} < a < 3^{n+2}\). For any element \(x\) in \(A\) (where \(x \neq 1\)), there exist \(s, t, p \in A\) such that \(x = s + t + p\). Find the minimum number of elements in the set \(A\).

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