
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, there are written 101 numbers: \(1^{2}, 2^{2}, \ldots, 101^{2}\). In one operation, it is allowed to erase any two numbers and write instead the absolute value of their difference.

What is the smallest number that can be obtained after 100 operations?

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