
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 $x, y$ satisfy the constraints $1 \leq x+y \leq 4$, $-2 \leq x-y \leq 2$. If the objective function $z=ax+y$ (where $a>0$) only reaches its maximum value at the point $(3,1)$, then the range of values for $a$ is ______.

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