
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 \(\alpha, \beta \in\left(0, \frac{\pi}{2}\right)\), the necessary and sufficient condition for \(\alpha + \beta = \frac{\pi}{2}\) is: \(\frac{\sin^{k+2} \alpha}{\cos^{k} \beta} + \frac{\cos^{k+2} \alpha}{\sin^{k} \beta} = 1\), where \(k \in \mathbf{N}^{*}\).

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