
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 an arithmetic sequence with $a\_1=2$ and $a\_1+a\_2+a\_3=12$.

1. Find the general term formula for the sequence $\{a\_n\}$ and the sum of its first $n$ terms $S\_n$.
2. Compute the value of $\frac{1}{S\_1} + \frac{1}{S\_2} + \frac{1}{S\_3} + \dots + \frac{1}{S\_{10}}$.

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