
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
Let vertices $A, B, C$, and $D$ form a regular tetrahedron with each edge of length 1 unit. Define point $P$ on edge $AB$ such that $P = tA + (1-t)B$ for some $t$ in the range $0 \leq t \leq 1$ and point $Q$ on edge $CD$ such that $Q = sC + (1-s)D$ for some $s$ in the range $0 \leq s \leq 1$. Determine the minimum possible distance between $P$ and $Q$.

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