
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 formula for the $n$-th term, $a_n$, and the sum of the first $n$ terms, $S_n$.  
(2) Calculate the value of $$\frac{1}{S_{1}} + \frac{1}{S_{2}} + \frac{1}{S_{3}} + \ldots + \frac{1}{S_{10}}.$$

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