
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 the function $y=f(x)$, where $f(1+x)=f(1-x)$ for all real numbers $x$, and $f(x)$ is monotonic on $[1,+\infty)$, if $f(a_{6})=f(a_{23})$ for an arithmetic sequence ${a_{n}}$ with non-zero common difference, find the sum of the first $28$ terms of the sequence ${a_{n}}$.

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