
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 such that
\begin{align*}
y+z & = \frac{22}{2}, \\
z+x & = \frac{24}{2}, \\
x+y & = \frac{26}{2}.
\end{align*}
Find $\sqrt{xyz(x+y+z)}$.

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