
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 complex numbers $z_1$ and $z_2$ which satisfy $z_1 = m + (4 - m^2)i$ and $z_2 = 2\cos \theta+( \lambda + 3\sin \theta)i$ where $m$, $\lambda$, $\theta \in \mathbb{R}$, and $z_1 = z_2$, determine the range of possible values for $\lambda$.

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