
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 of complex numbers \( M=\{z \mid z=\cos \alpha+(4-\cos^2 \alpha)i, \alpha \in \mathbf{R} \} \) and \( N=\{z \mid z=\cos \beta+(\lambda+\sin \beta)i, \beta \in \mathbf{R} \} \), find the range of the real number \(\lambda\) when \( M \cap N \neq \varnothing \).

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