
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 sets M and N are defined as \( M=\left\{z \left\lvert\, z=\frac{t}{1+t}+i \frac{1+t}{t}\right., t \in \mathbf{R}, t \neq-1, t \neq 0\right\} \) and \( N=\{z \mid z=\sqrt{2}[\cos (\arcsin t)+i \cos (\arccos t)], t \in \mathbf{R},|t| \leqslant 1\} \), calculate the number of elements in \( M \cap N \).

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