
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
Let $(x,y)$ satisfy the constraints $\begin{cases} 8x - y - 4 \leqslant 0 \\ x + y + 1 \geqslant 0 \\ y - 4x \leqslant 0 \end{cases}$, and the maximum value of the objective function $z = ax + by (a > 0, b > 0)$ is $2$. Find the minimum value of $\frac{1}{a} + \frac{1}{b}$.

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