
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 of radius \( r \) touching the base of the pyramid at points belonging to the segment connecting the midpoints of opposite sides of the base. Each of the spheres touches a lateral face of the pyramid and the other sphere. Find the height of the pyramid that minimizes the volume of the pyramid.

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