
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   $1\leq a<b\leq 100$ . If there exists a positive integer  $k$  such that  $ab|a^k+b^k$ , we say that the pair  $(a, b)$  is good. Determine the number of good pairs.

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