
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
An open box is constructed from a rectangular metal sheet measuring \( 20 \) in. by \( 30 \) in. Squares with side length \( x \) inches are cut from each of the four corners. The flaps are then folded up to form the sides of the box. To ensure that the box can be formed without any piece overlapping, \( x \) must be less than half the smaller dimension of the metal sheet. Find an expression for the volume of the box.
A) \( 600x - 100x^2 + 4x^3 \)  
B) \( 600x + 100x^2 + 4x^3 \)  
C) \( 300x - 50x^2 + 2x^3 \)  
D) \( 300x + 150x^2 + 6x^3 \)  
E) \( 400x - 80x^2 + 3x^3 \)

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