
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
For an arithmetic sequence $\{a_n\}$ with a non-zero common difference, if $a_1^2+a_7^2=a_3^2+a_9^2$, and the sum of the first $n$ terms of $\{a_n\}$ is denoted as $s_n$, where $s_8=8$, then the general formula for $\{a_n\}$ is $a_n=$

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