
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
When making an open-top box from a square sheet of iron with a side length of $36\,cm$, by cutting out a small square of equal area from each of the four corners and then folding up the sides, the volume of the box made is maximized. What is the side length of the small square cut out from each corner?

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