
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) Calculate the value of $\frac{1}{S_1} + \frac{1}{S_2} + \frac{1}{S_3} + \cdots + \frac{1}{S_{10}}$.

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