
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 $D$ each edge having length 2, find the least possible distance between points $P$ and $Q$, where $P$ is on edge $AB$ at a distance $t$ from $A$ and $1-t$ from $B$, and $Q$ is on edge $CD$ at a distance $s$ from $C$ and $1-s$ from $D$, as $t$ and $s$ vary between 0 and 1.

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