
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 a complex number $z=\frac{{-3+i}}{{{i^7}}}$.  
$(1)$ Find $z$;  
$(2)$ If the complex numbers $z$ and $2-i$ correspond to the vectors $\overrightarrow{OA}$ and $\overrightarrow{OB}$ in the complex plane, respectively, find the complex number corresponding to the vector $\overrightarrow{AB}$.

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