
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 $(x,y)$ satisfies $\begin{cases} & 2x+y\leqslant 4 \ \\ & x\leqslant y \ \\ & x\geqslant \frac{1}{2} \end{cases}$, then the maximum value of $z=2x-y$ is _______.

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