
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, and $a_1=2$, $a_1+a_2+a_3=12$.
(1) Find the general term formula for the sequence $\{a_n\}$ and the sum of the first $n$ terms, $S_n$;
(2) Calculate the value of $\frac{1}{S_1} + \frac{1}{S_2} + \frac{1}{S_3} + \ldots + \frac{1}{S_{100}}$.

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