
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
The following arrays are each composed of three numbers: $(1,2,-1)$, $(2,4,-2)$, $(3,8,-5)$, $(4,16,-12)$, $(5,32,-27)$, ... $(a_{n},b_{n},c_{n})$. If the sum of the first $n$ terms of the sequence $\{c_{n}\}$ is $S_{n}$, then $S_{10}=$ _____ .

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