
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 \( x, y, z \) be the lengths of the midline segments connecting the midpoints of opposite edges of a tetrahedron \( P-ABC \). If the sum of the squares of the six edge lengths of the tetrahedron is 300, find \( x^{2} + y^{2} + z^{2} \).

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