
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 $\left\{a_{n}\right\}$ with a common difference $d \neq 0$, and $a_{5}^{2}+a_{7}^{2}+16 d=a_{9}^{2}+a_{11}^{2}$, find the sum of the first 15 terms, $S_{15}$, of the sequence.

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