
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
Let $\{a\_n\}$ be an arithmetic sequence, and $\{b\_n\}$ be a geometric sequence with all positive terms. Given that $a\_1 = b\_1 = 1$, $a\_3 + b\_5 = 21$, and $a\_5 + b\_3 = 13$.

1. Find the general term formulas for the sequences $\{a\_n\}$ and $\{b\_n\}$.
2. Let $S\_n$ denote the sum of the first $n$ terms of the sequence $\{\frac{a\_n}{b\_n}\}$. Compare $S\_n$ with $6$.

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