
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
Find the maximum and minimum values of the function \(z = f(x, y) = x^3 + y^3 + 6xy\) within the rectangle with vertices at \(A(-3, -3)\), \(B(-3, 2)\), \(C(1, 2)\), and \(D(1, -3)\).

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