
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
In the arithmetic sequence $\{a_n\}$,  
(1) it is known that $a_4 + a_{14} = 2$, find $S_{17}$;  
(2) it is known that $a_{11} = 10$, find $S_{21}$;  
(3) it is known that $S_{11} = 55$, find $a_6$;  
(4) it is known that $S_8 = 100$ and $S_{16} = 392$, find $S_{24}$.

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