
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 points $A(-3,0), B(-1,-2)$, if there are exactly two points $M, N$ on the circle ${(x-2)}^{2}+{y}^{2}={r}^{2} (r > 0)$ such that the areas of $\triangle MAB$ and $\triangle NAB$ are both $4$, then the range of $r$ is \_\_\_\_.

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