
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
Given a regular tetrahedron with vertices \(A\), \(B\), \(C\), and \(D\) where each edge measures 2 units, find the least possible distance between points \(P\) and \(Q\), where \(P\) divides \(AB\) in the ratio 1:3, and \(Q\) divides \(CD\) in the ratio 2:1, respectively from \(A\) and \(C\).

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