
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 2, such that
\[
\frac{(x + 3)^2}{y + z - 3} + \frac{(y + 5)^2}{z + x - 5} + \frac{(z + 7)^2}{x + y - 7} = 45.
\]
Find the ordered triple $(x, y, z)$.

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