
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
Let \( O x, O y, O z \) be three rays, and \( G \) a point inside the trihedron \( O x y z \). Consider all planes passing through \( G \) and cutting \( O x, O y, O z \) at points \( A, B, C \), respectively. How is the plane to be placed in order to yield a tetrahedron \( O A B C \) with minimal perimeter?

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