
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 a sequence $\left\{ b_n \right\}$ satisfying $b_1=\frac{1}{2}$, $2b_{n+1}-b_n\cdot b_{n+1}=1$, calculate the value of $b_1+\frac{b_2}{2^2}+\frac{b_3}{3^2}+\cdots +\frac{b_{100}}{100^2}$.

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