
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
Let \( a \) and \( b \) be positive integers such that:
- \( \gcd(a+b, 330) = 1 \),
- \( a^a \) is a multiple of \( b^b \),
- \( a \) is not a multiple of \( b \).
Find the smallest possible value of \( a+b \).

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