
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 a positive integer $\mathrm{n}$ such that $n \geq 2$, the set $\mathrm{A}$ contains only positive integers, with the smallest element being $1$ and the largest element being $a$, where $7 \times 3^{n}<a<3^{n+2}$. For any element $x$ in $\mathrm{A}$ (where $x \neq 1$), there exist $y, z, w \in A$ (which can be the same) such that $x = y + z + w$. Find the minimum number of elements in set $\mathrm{A}$.

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