
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 \(A B C D\), a line \(M P\) is drawn through the midpoint \(M\) of edge \(A B\) and the centroid \(P\) of face \(B C D\). Another line \(N Q\) passes through the midpoint \(N\) of edge \(B C\) and the centroid \(Q\) of face \(A B D\). Calculate the angle between the lines \(M P\) and \(N Q\).

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