
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 the point $\left(4a,2b\right)\left(a \gt 0,b \gt 0\right)$ lies on the common chord of circles $C:x^{2}+y^{2}=4$ and $M:\left(x-2\right)^{2}+\left(y-2\right)^{2}=4$, 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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