
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
Now Wendy wanders over and joins Dr. Lisi and her younger siblings.  Thinking she knows everything there is about how to work with arithmetic series, she nearly turns right around to walk back home when Dr. Lisi poses a more challenging problem.  "Suppose I select two distinct terms at random from the  $2008$  term sequence.  What's the probability that their product is positive?"  If  $a$  and  $b$  are relatively prime positive integers such that  $a/b$  is the probability that the product of the two terms is positive, find the value of  $a+b$ .

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