
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 two sets \( M = \left\{ z \mid z = \frac{t}{1+t} + i \frac{1+t}{t}, t \in \mathbb{R}, t \neq -1, t \neq 0 \right\} \) and \( N = \left\{ z \mid z = \sqrt{2}[\cos (\arcsin t) + i \cos (\arccos t)], t \in \mathbb{R}, |t| \leq 1 \right\} \), determine the number of elements in the intersection \( M \cap N \).

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