
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
If the function $f$ satisfies $f\left(\frac{x}{x-1}\right) = \frac{1}{x}$ for all real numbers $x \neq 0, 1$, and $0 < \theta < \frac{\pi}{2}$, find the value of $f\left(\sec^2 \theta\right)$.

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