
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 the arithmetic sequence $\left\{ {{a}\_{n}} \right\}$ with first term ${{a}\_{1}}=2$ and common difference $d=2$, let ${{S}\_{n}}$ denote the sum of its first $n$ terms. Find the sum of the first $100$ terms of the sequence $\left\{ \frac{1}{{{S}\_{n}}} \right\}$.

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