
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 the function \( y = f(x) \) with its inverse function \( g(x) = \log _{\sin ^{2} \theta}\left(\frac{1}{x}-\cos ^{2} \theta\right) \) (where the constant \(\theta \in\left(0, \frac{\pi}{2}\right)\)), find the solution set for the equation \( f(x) = 1 \).

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