
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 \(ABCD\), \(MN\) is the line segment joining the midpoint of \(AD\) and the centroid of \(\triangle BCD\). \(PQ\) is the line segment joining the midpoint of \(CD\) and the centroid of \(\triangle ABC\). Find the angle between the lines \(MN\) and \(PQ\).

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