
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) Given $a_4 + a_{14} = 2$, then $S_{17} = \_\_\_\_\_\_\_\_$;  
(2) Given $a_{11} = 10$, then $S_{21} = \_\_\_\_\_\_\_\_$;  
(3) Given $S_{11} = 55$, then $a_6 = \_\_\_\_\_\_\_\_$;  
(4) Given $S_8 = 100$ and $S_{16} = 392$, then $S_{24} = \_\_\_\_\_\_\_\_$.

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