
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
Suppose the first term of an increasing arithmetic sequence $\{a\_n\}$ is $a\_1=1$, and $a\_1$, $a\_2$, $a\_4$ form a geometric sequence. Find the sum of the first 10 terms of the sequence, denoted as $S\_10$.

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