
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<sub>n</sub>} that satisfies a<sub>2</sub>+a<sub>5</sub>+a<sub>9</sub>\=a<sub>6</sub>+8, find the value of a<sub>5</sub>. If a<sub>1</sub>\=16, find the value of n when the sum of the first n terms of the sequence reaches its maximum value.

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