
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
Find  $ \sum_{k \in A} \frac{1}{k-1}$  where  $A= \{ m^n : m,n \in \mathbb{Z} m,n \geq 2 \} $ .

Problem was post earlier [here](http://www.artofproblemsolving.com/Forum/viewtopic.php?f=67&t=29456&hilit=silk+road) , but solution not gives and olympiad doesn't indicate, so I post it again  :blush:

Official solution [here](http://www.artofproblemsolving.com/Forum/viewtopic.php?f=125&t=365714&p=2011659#p2011659)

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