
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 four terms of the arithmetic sequence $\\{a\_n\\}$ is $10$, and $a\_2$, $a\_3$, $a\_7$ form a geometric sequence.

$(1)$ Find the general term formula $a\_n$.
$(2)$ Let $b\_n=2^{a\_n}$, find the sum of the first $n$ terms of the sequence $S\_n$.

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