
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 has length 2. Find the minimum possible distance between a pair of points $P$ and $Q$, where $P$ is located one-fourth of the way from $A$ to $B$ and $Q$ is located three-fourths of the way from $C$ to $D$.

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