
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
A grid rectangle with sides 629 and 630 is divided into several squares (all cuts are along the grid lines). What is the smallest number of squares with odd side lengths that can appear in such a division? Don't forget to explain why it's not possible to have fewer squares with odd side lengths in the division.

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