
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 the sequence {a<sub>n</sub>} that satisfies $$a_{1}=- \frac {1}{9}$$ and $$a_{n+1}= \frac {a_{n}}{8a_{n}+1}$$ (n∈N<sup>\*</sup>), find the maximum value of the terms in {a<sub>n</sub>}.

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