
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 $PR=QS=26$, $PS=RQ=42$, and $PQ=RS=50$. For any point $Y$ in space, we define $g(Y)=PY+QY+RY+SY$. Find the least possible value of $g(Y)$, which can be expressed as $a\sqrt{b}$ for positive integers $a$ and $b$, where $b$ is not divisible by the square of any prime. Compute $a+b$.

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