
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
Determine the largest real number  $z$  such that
\begin{align*}
x + y + z = 5 
xy + yz + xz = 3
\end{align*}
and  $x$ ,  $y$  are also real.

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