
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 variables $x$, $y$, satisfying the constraints
$$
\begin{cases}
& x-1\geqslant 0 \\
& 2x-y-1\leqslant 0 \\
& x+y-3\leqslant 0 \\
\end{cases},
$$
then the minimum value of $z=x-y$ is $\boxed{-1}$.

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