
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 value of $z = x - 2y$ for real numbers $x$ and $y$ satisfying the constraints:
$$
\begin{cases}
x \geqslant 0 \\
y \geqslant 0 \\
2x + y \leqslant 2
\end{cases}
$$

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