
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 sum of the first $n$ terms of the sequence $\{a_{n}\}$ is $S_{n}=-\frac{1}{2}n^2-\frac{1}{2}n$, and the sequence $\{b_{n}\}$ satisfies $b_{n}={2}^{a_{n}}$, find $\underset{lim}{n→∞}(b_{1}+b_{2}+\cdots +b_{n})$.

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