
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
If the real numbers $x$ and $y$ satisfy the system of inequalities $\begin{cases} \begin{matrix} x - y - 2 \geqslant 0 \\ 2x + y - 2 \leqslant 0 \\ \end{matrix} \\ y + 4 \geqslant 0, \end{cases}$ then the maximum value of the objective function $z = 4x + 3y$ is $(\quad\quad)$.

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