
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
The real number solution \((x, y, z)\) of the equation \(2 \sqrt{x-4} + 3 \sqrt{y-9} + 4 \sqrt{z-16} = \frac{1}{2}(x + y + z)\) is \(\qquad\)

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