
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 the sequence $\{a_n\}$, where $a_1=1$, and $$a_{n-1}-a_{n}=a_{n-1}a_{n} \quad (n\geq2, n\in\mathbb{N}^{*})$$, let $b_n=a_{2n-1}a_{2n+1}$, then the sum of the first 100 terms of the sequence $\{b_n\}$ is \_\_\_\_\_\_.

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