
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 $z_{1}=x-1+yi$ and $z_{2}=1+\left(4-y\right)i$, where $x$ and $y$ are real numbers.  
$(1)$ If $z_{1}=z_{2}$, find $|z_{1}|$.  
$(2)$ If $x=y=3$, calculate $\frac{{z_2^2}}{{{z_1}+{z_2}}}$.

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