
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
Two regular tetrahedrons $A B C D$ and $M N P Q$ are positioned such that the planes $B C D$ and $N P Q$ coincide, the vertex $M$ lies on the height $A O$ of the first tetrahedron, and the plane $M N P$ passes through the center of the face $A B C$ and the midpoint of the edge $B D$. Find the ratio of the edge lengths of the tetrahedrons.

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