
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 \( M=\{(x, y) \mid \tan(\pi y) + \sin^2(\pi x) = 0\} \) and \( N=\{(x, y) \mid x^{2}+y^{2} \leq 2\} \), calculate the number of elements in the intersection \( M \cap N \).

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