
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 $x,$ $y,$ $z$ be real numbers, all greater than 3, so that
\[\frac{(x + 4)^2}{y + z - 4} + \frac{(y + 6)^2}{z + x - 6} + \frac{(z + 8)^2}{x + y - 8} = 48.\]Enter the ordered triple $(x,y,z).$

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