
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
We define  $N$  as the set of natural numbers  $n<10^6$  with the following property:

There exists an integer exponent  $k$  with  $1\le k \le 43$ , such that  $2012|n^k-1$ .

Find  $|N|$ .

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