
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
Let S<sub>n</sub> be the sum of the first n terms of the arithmetic sequence {a<sub>n</sub>}. Given that S<sub>9</sub> = ‒a<sub>5</sub>.

1. If a<sub>3</sub> = 4, find the general term formula for {a<sub>n</sub>}.
2. If a<sub>1</sub> > 0, find the range of n for which S<sub>n</sub> ≥ a<sub>n</sub>.

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