
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 an increasing arithmetic sequence $\{a\_n\}$, $a\_3=1$, and $a\_4$ is the geometric mean of $a\_3$ and $a\_7$.
(I) Find the general term formula of the sequence $\{a\_n\}$;
(II) Let $S\_n$ denote the sum of the first $n$ terms of the sequence $\{a\_n\}$. Find the value of $S\_10$, the sum of the first 10 terms.

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