
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 side of the base \(ABCD\) of the regular pyramid \(SABCD\) is \(8\), and the height \(SO\) is \(3\). Point \(M\) is the midpoint of edge \(SB\), and point \(K\) is the midpoint of edge \(BC\). Find:
1) The volume of the pyramid \(AMSK\);
2) The angle between the lines \(AM\) and \(SK\);
3) The distance between the lines \(AM\) and \(SK\).

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