
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
Given the curve $x^2-y^2=0$ and the directrix of the parabola $y^2=-4x$ form a triangular region $D$, and $P(x, y)$ is a moving point within $D$, find the maximum value of the objective function $z=x-2y+5$.

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