
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
Consider a regular tetrahedron with vertices \(A\), \(B\), \(C\), and \(D\), where each edge of the tetrahedron is of length 1. Let \(P\) be a point on edge \(AB\) such that \(AP = t \times AB\) and \(Q\) be a point on edge \(CD\) such that \(CQ = s \times CD\), where \(0 \leq t, s \leq 1\). Find the least possible distance between points \(P\) and \(Q\).

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