
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
A positive integer  $n$  between  $1$  and  $N=2007^{2007}$  inclusive is selected at random.  If  $a$  and  $b$  are natural numbers such that  $a/b$  is the probability that  $N$  and  $n^3-36n$  are relatively prime, find the value of  $a+b$ .

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