
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 arithmetic mean of four numbers is 20. Three of the numbers are 12, 24, and 36, and the fourth number is the square of another number. What is the fourth number?

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