
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 $ABCD$ with edge length $a$, point $M$ is the midpoint of $AB$ and point $K$ is the midpoint of $CD$. Find the angle and the distance between lines $CM$ and $BK$. In what ratio does the common perpendicular to these lines divide the segment $CM$ and $BK$?

Through the midpoint of the height of a regular quadrilateral pyramid, a cross-section is made perpendicular to the lateral edge. Find the area of this section if the lateral edge is 4 and the angle between the lateral edges lying in one face is $\frac{\pi}{3}$.

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