
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 line $2ax - by + 2 = 0$ ($a > 0, b > 0$) and the circle $(x + 1)^2 + (y - 2)^2 = 4$, the chord length formed by the intersection of the line and the circle is $4$. Find the minimum value of $\frac{1}{a} + \frac{1}{b}$.

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