
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 a circle $x^2+y^2+2x-4y+1=0$ and any point on the circle, if the symmetric point about the line $2ax-by+2=0$ ($a, b \in \mathbb{R}^+$) is still on the circle, then the minimum value of $\frac{1}{a} + \frac{2}{b}$ is \_\_\_\_\_\_.

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