
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 that $x$ and $y$ satisfy the constraints $\begin{cases} x - y - 1 \leqslant 0 \\ 2x - y - 3 \geqslant 0 \end{cases}$, when the objective function $Z = ax + by$ ($a > 0$, $b > 0$) takes the minimum value of $3$ under these constraints, the minimum value of $\frac{2}{a} + \frac{1}{b}$ is

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