
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
In $\triangle ABC$, it is given that $\cos B \cos C \sin^{k} \frac{A}{2} + \cos C \cos A \sin^{k} \frac{B}{2} + \cos A \cos B \sin^{k} \frac{C}{2} < 1$, where $k \geq 0$.

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