
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 complex numbers $z_{1}=4-m^{2}+(m-2)i$ and $z_{2}=\lambda +\sin \theta +(\cos \theta -2)i$, where $i$ is the imaginary unit, and $m$, $\lambda$, $\theta \in \mathbb{R}$.  
$(Ⅰ)$ If $z_{1}$ is purely imaginary, find the value of $m$.  
$(Ⅱ)$ If $z_{1}=z_{2}$, find the range of values for $\lambda$.

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