
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 $a$, $b$, and $c$ are non-zero rational numbers, and satisfy $a{b^2}=\frac{c}{a}-b$, then $({\frac{{{a^2}{b^2}}}{c^2}-\frac{2}{c}+\frac{1}{{{a^2}{b^2}}}+\frac{2ab}{c^2}-\frac{2}{abc}})÷({\frac{2}{ab}-\frac{2ab}{c}})÷\frac{101}{c}$ is equal to ______.

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