
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 sequence $\{a\_n\}$ is a geometric sequence with a positive common ratio, $a\_1=2$, and $a\_3-a\_2=12$.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. If the sequence $\{b\_n\}$ satisfies $b\_n=\log _{3}( \frac {3^{n}}{2})+\log _{3}a\_n$, find the sum of the first $n$ terms, $S\_n$, for the sequence $\{a\_n+b\_n\}$.

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