
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
A cube is inscribed in a cone (one of the faces of the cube lies in the plane of the base of the cone). The ratio of the height of the cone to the edge of the cube is $k$. Find the angle between the generatrix and the height of the cone.

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