
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
In a white $10 \times 10$ square, on the first move, a $1 \times 1$ checkered rectangle is painted, on the second move a $1 \times 2$ checkered rectangle is painted, on the third move a $1 \times 3$ checkered rectangle is painted, and so on, as long as it is possible to do so. After what minimum number of moves could this process end? (Cells cannot be painted again.)

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