
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
Let \( f(x) = \frac{\sin^m x}{a} + \frac{b}{\sin^n x} \), where \( a, b, m, n \in \mathbf{N}^{*} \) and \( x \in (0, \pi) \). Find the minimum value of \( f(x) \).

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