
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
In a regular tetrahedron \( P-ABCD \), where each face is an equilateral triangle with side length 1, points \( M \) and \( N \) are the midpoints of edges \( AB \) and \( BC \), respectively. Find the distance between the skew lines \( MN \) and \( PC \).

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