
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 \(12^4\) is written out in base 10, the sum of its digits is $25=5^2$. What is the largest base \(b\) such that the base-\(b\) digits of \(12^4\) do not add up to $5^2$? (Note: Here, \(12^4\) in base \(b\) means that the base-\(b\) number \(12\) is raised to the fourth power.)

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