
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 \(ABCD\), the line segment \(MN\) connects the midpoint of edge \(AD\) and the centroid of face \(BCD\), and the line segment \(PQ\) connects the midpoint of edge \(CD\) and the centroid of face \(ABC\). Find the angle between \(MN\) and \(PQ\).

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