
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
Let the set $M=\{(x,y)|x^2+y^2\leq 4\}$, and $N=\{(x,y)|(x-1)^2+(y-1)^2\leq r^2\}$ where $r>0$. When $M\cap N=N$, the range of the real number $r$ is \_\_\_\_\_\_.

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