
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
Given that Henry's three brothers have ages that are distinct single-digit positive integers, one brother is twice as old as another, and the square of the youngest brother's age is equal to the age of the other brother, calculate the sum of the ages of Henry's three brothers.

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