
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
On a board, the numbers \( \frac{1}{1}, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \ldots, \frac{1}{100} \) are written.

It is allowed to erase any two numbers \( a \) and \( b \) and write in their place \( ab + a + b \).

Then, proceed similarly with any two of the remaining numbers, and so on. What number can remain as the last one?

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