
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 the non-empty set
$$
A=\left\{(x, y) \left\lvert\,\left\{\begin{array}{l}
a x-2 y+8 \geqslant 0, \\
x-y-1 \leqslant 0, \\
2 x+a y-2 \leqslant 0
\end{array}\right\} .\right.\right.
$$

When $(x, y) \in A$, the function $z=y-x$ has both a maximum value and a minimum value. Determine the range of the real number $a$.

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