
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 that the sum of the first $n$ terms of the geometric sequence $\{a\_n\}$ is $S\_n$, with $a\_1 = 1$ and $S\_6 = 9S\_3$:

1. Find the general term formula for $\{a\_n\}$;
2. Let $b\_n = 1 + \log\_2 a\_n$, find the sum of the first $n$ terms of the sequence $\{b\_n\}$.

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