
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 base radius of cylinder $M$ is $2$, and its height is $\frac{2\sqrt{3}}{3}$, the diameter of the base of cone $N$ is equal to the length of its slant height. If the volume of cylinder $M$ is equal to that of cone $N$, find the base radius of cone $N$.

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