
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
In a Cartesian coordinate system on a plane, let O(0,0), M(1,1), N(0,1), and Q(2,-3) be points on the plane. A moving point P(x, y) satisfies the inequalities $0 \leq x \leq 1$ and $0 \leq y \leq 1$. Find the maximum value of $z = x^2 + y^2$.

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