
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 sequences $\left\{a_{n}\right\}$ and $\left\{b_{n}\right\}$ are both arithmetic series, with $a_{11}=32$ and $b_{21}=43$. Define $c_{n}=(-1)^{n} \cdot\left(a_{n}-b_{n}\right)$. The sum of the first 10 terms of the sequence $\left\{c_{n}\right\}$ is 5, and the sum of the first 13 terms is -5. What is the sum of the first 100 terms of the sequence $\left\{b_{n}\right\}$?

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