
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 real numbers \(x, y\) satisfying the constraints
\[
\begin{cases} 
y \geqslant 1 \\
y \leqslant 2x - 1 \\
x + y \leqslant m \\
\end{cases}
\]
If the minimum value of \(z = x - y\) is \(0\), then the real number \(m =\) \_\_\_\_\_\_\_.

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