
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 the geometric sequence $\{a\_n\}$ with $a\_1=2$ and $a\_2=4(a\_3-a\_4)$, and the sequence $\{b\_n\}$ with $b\_n=3-2\log\_2 a\_n$.

1. Find the general term formula for the sequences $\{a\_n\}$ and $\{b\_n\}$.
2. Let $c\_n=\frac{b\_n}{a\_n}$. Find the sum $S\_n$ of the first $n$ terms of the sequence $\{c\_n\}$.

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