
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 $\{a_{n}\}$ satisfies $a_{1}=2$, $a_{2}=1$, and $\frac{a_{n-1}-a_{n}}{a_{n} \cdot a_{n-1}}=\frac{a_{n}-a_{n+1}}{a_{n} \cdot a_{n+1}}(n \geqslant 2)$, find the $100^{th}$ term of the sequence $\{a_{n}\}$.

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