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

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