
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 $$(x+y+z)(xy+xz+yz)=45$$ and $$x^2(y+z)+y^2(x+z)+z^2(x+y)=15$$ for real numbers $x$, $y$, and $z$, and additionally, $x+y+z = 5$, find the value of $xyz$.

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