
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 that the complex numbers $z_{1}$, $z_{2}$, $z_{3}$ in the complex plane correspond to points $A(-1,1)$, $B(1,2)$, $C(-2,-1)$.  
$(1)$ Find the values of $z_{2}+z_{3}$ and $\frac{{z_{2}}}{{z_{1}}}$.  
$(2)$ Find $\cos \angle ABC$.

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