
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
Given an arithmetic sequence {a_n} with the sum of its first n terms denoted as S_n, and given that a_1008 > 0 and a_1007 + a_1008 < 0, find the positive integer value(s) of n that satisfy S_nS_{n+1} < 0.

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