
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 piece of cardboard with a length of $80cm$ and a width of $60cm$ is used to cut out four identical small squares from the four corners. Then, a lidless rectangular paper box with a base area of $1500cm^{2}$ is made. Find the side length of the small square that was cut out.

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