
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
What can be the edge length of a cube, one face of which lies in the plane of the base of a regular quadrilateral pyramid, while the four remaining vertices are on its lateral surface, given that the sides of the base of the pyramid are equal to \(a\) and the height of the pyramid is \(h\)?

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