
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
The relationship between the volume $V(x)$ of a certain box and the length $x$ of its base side is given by $$V(x)=x^{2}\cdot \left( \frac {60-x}{2}\right)$$, find the length of the box's base side when the volume of the box is at its maximum.

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