
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 that the sequence {a<sub>n</sub>} is an arithmetic sequence, a<sub>1</sub> < 0, a<sub>8</sub> + a<sub>9</sub> > 0, a<sub>8</sub> • a<sub>9</sub> < 0. Find the smallest value of n for which S<sub>n</sub> > 0.

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