
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
For all real numbers $x$ except $x=0$ and $x=1$, the function $f(x)$ is defined by
\[f \left( \frac{x}{x-1} \right) = \frac{1}{x}.\]
Suppose $0 \leq t \leq \frac{\pi}{2}$. What is the value of $f(\tan^2 t)$?

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