
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
Use \((a, b)\) to represent the greatest common divisor of \(a\) and \(b\). Let \(n\) be an integer greater than 2021, and \((63, n+120) = 21\) and \((n+63, 120) = 60\). What is the sum of the digits of the smallest \(n\) that satisfies the above conditions?

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