
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
Under the constraints $\left\{\begin{array}{l}x \geq 0 \\ y \geq 0 \\ x+y \leq s \\ y+2x \leq 4 \end{array}\right.$, when $3 \leq s \leq 5$, find the range of the maximum value of the objective function $z=3x+2y$.

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