
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
Given that $$(x+y+z)^2 = 25$$ and that $$(xy+xz+yz) = 8,$$ for real numbers $x$, $y$, and $z$, calculate the value of $$x^2 + y^2 + z^2.$$

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