
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 \( ABCD \) has \( AD = BC = 30 \), \( AC = BD = 46 \), and \( AB = CD = 50 \). For any point \( X \) in space, let \( g(X) = AX + BX + CX + DX \). Determine the least possible value of \( g(X) \).

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