
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 that $0 < k < 2$, find the maximum and minimum values of $\cos (β-γ)$ if the following equations hold:

$$\cos α+k\cos β+(2-k)\cos γ=0$$
$$\sin α+k\sin β+(2-k)\sin γ=0$$

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