
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
1. In the geometric sequence $\{a\_n\}$, $a\_5=162$, the common ratio $q=3$, and the sum of the first $n$ terms $S\_n=242$. Find the first term $a\_1$ and the number of terms $n$.
2. There are four numbers. The product of the first three numbers is 216, which forms a geometric sequence, and the sum of the last three numbers is 36, which forms an arithmetic sequence. Find these four numbers.

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