
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 balloon is placed inside a cubic frame with edge length $a$ such that it is inflated as much as possible while still maintaining its spherical shape. What is the maximum value of the balloon's surface area?

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