
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-negative real numbers $x$ and $y$ that satisfy the constraints:
$$
\begin{cases}
x+y-3 \leq 0 \\
2x+y-4 \geq 0
\end{cases}
$$
find the maximum value of $z=2x+3y$.

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