
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 sequence $\{a\_n\}$ that satisfies the equation: $a\_1 + 3a\_2 + 3^2a\_3 + \dots + 3^{n-1}a\_n = n$, where $n \in \mathbb{N}^*$.

1. Find the general term of the sequence $\{a\_n\}$.
2. If sequence $\{b\_n\}$ satisfies $3^{b\_n} = \frac{3}{a\_n}$, find the sum of the first $n$ terms, denoted as $S\_n$, of the sequence $\{ \frac{b\_n}{a\_n} \}$.

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