
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
If the variables $x,y$ satisfy the constraints
\[
\begin{cases}
& y\leqslant 1, \\
& x+y\geqslant 0, \\
& x-y-2\leqslant 0, \\
\end{cases}
\]
then the maximum value of $z=x-2y$ is     .

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