
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
\[ f\left(\frac{x}{x-1}\right) = \frac{1}{x^2}. \]
Suppose \( 0 \leq t \leq \frac{\pi}{4} \). What is the value of \( f(\tan^2 t) \)?

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