
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 \( x \) and \( y \) satisfy the constraints:
\[
\begin{cases}
x - y - 2 \geq 0, \\
x - 5 \leq 0, \\
y + 2 \geq 0.
\end{cases}
\]
Then, the sum of the minimum and maximum values of \( z = x^2 + y^2 \) is \(\quad\)

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