
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 $y$ that satisfy the system of inequalities $\begin{cases} x - 2y - 2 \leqslant 0 \\ x + y - 2 \leqslant 0 \\ 2x - y + 2 \geqslant 0 \end{cases}$, if the minimum value of the objective function $z = ax + by + 5 (a > 0, b > 0)$ is $2$, determine the minimum value of $\frac{2}{a} + \frac{3}{b}$.

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