
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 the function f(x) is monotonous on (1,+∞), if the sequence {a<sub>n</sub>} is an arithmetic sequence with a non-zero common difference, and f(a<sub>4</sub>)=f(a<sub>18</sub>), calculate the sum of the first 21 terms of {a<sub>n</sub>}.

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