
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 that the graph of the function $y=f(x+1)$ is symmetric about the $y$-axis and that the function $f(x)$ is monotonic on $(1,+\infty)$, if the sequence $\{a_n\}$ is an arithmetic sequence with a non-zero common difference and $f(a_6)=f(a_{20})$, calculate the sum of the first 25 terms of the sequence $\{a_n\}$.

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