
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 $x$ and $y$ satisfy the linear constraints $x+y-4 \geq 0$ and $2x-y-5 \leq 0$, the objective function $z = y - ax$ ($a \in \mathbb{R}$). If the unique optimal solution for $z$ to achieve its maximum value is $(1,3)$, determine the range of the real number $a$.

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