
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
Find the edge of a cube, one face of which lies in the plane of the base of a regular triangular pyramid, and the remaining four vertices are on its lateral surface, if the sides of the base of the pyramid are equal to $a$, and the height of the pyramid is equal to $h$.

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