
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 tetrahedron $PQRS$ have side lengths $PQ = RS = 30$, $PR = QS = 46$, and $PS = QR = 50$. Define the function $g(X) = PX + QX + RX + SX$ for any point $X$ in space. Determine the least possible value of $g(X)$, which can be expressed as $a\sqrt{b}$, where $a$ and $b$ are positive integers, and $b$ is not divisible by the square of any prime. Find $a+b$.

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