
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 $D$, and each edge of length 1, find the least possible distance between a pair of points $P$ and $Q$, where $P$ is $\frac{1}{3}$ of the way from $A$ to $B$, and $Q$ is $\frac{2}{3}$ of the way from $C$ to $D$.

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