
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
The base of pyramid \( A B C S \) is an equilateral triangle \( A B C \) with a side length of \( 4 \sqrt{2} \). The lateral edge \( S C \) is perpendicular to the base plane and has a length of 2. Find the angle and the distance between the skew lines, one of which passes through point \( S \) and the midpoint of edge \( B C \), and the other passes through point \( C \) and the midpoint of edge \( A B \).

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