
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 a regular quadrilateral pyramid, there are two identical spheres with radius \( r \), whose centers lie on the symmetry axis of the pyramid. One of the spheres touches all the lateral faces of the pyramid, and the second one touches the base of the pyramid and the first sphere. Find the height of the pyramid for which the volume of the pyramid is minimal.

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