
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
Tetrahedron $PQRS$ has $PR=QS=26$, $PS=QR=34$, and $PQ=RS=50$. For any point $X$ in space, suppose $g(X) = PX + QX + RX + SX$. Find the least possible value of $g(X)$ which can be expressed as $m\sqrt{n}$, where $m$ and $n$ are positive integers, and $n$ is not divisible by the square of any prime.

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