
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 square iron sheet with a side length of 48 cm has a small square with a side length of x cm cut off from each of its four corners (the four small squares cut off are congruent). Then, a lidless square box is made.
(1) Express the volume V of the box as a function of x;
(2) Find the maximum volume V of the box, and determine the value of x at which the maximum volume occurs.

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