
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
Among all solutions of the system

$$
\begin{aligned}
& x^{2}+y^{2}=4 \\
& z^{2}+t^{2}=9 \\
& x t+y z=6
\end{aligned}
$$

select those for which the value of $x+z$ is the maximum.

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