
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 the sets $M=\{(x,y)|y-1=k(x+1), x, y \in \mathbb{R}\}$ and $N=\{(x,y)|x^2+y^2-2y=0, x, y \in \mathbb{R}\}$, find the number of elements in the intersection of M and N.

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