
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 \( SABC \) is an isosceles right triangle \( ABC \) with the length of the hypotenuse \( AB = 4\sqrt{2} \). The lateral edge \( SC \) of the pyramid is perpendicular to the base plane, and its length is 2. Find the angle and the distance between two lines, one of which passes through point \( S \) and the midpoint of edge \( AC \), and the other passes through point \( C \) and the midpoint of edge \( AB \).

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