
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
In the complex plane, $O$ is the origin, and the complex number corresponding to vector $\overrightarrow{OA}$ is $2+i$.  
$(1)$ If point $A$ is symmetric to the real axis at point $B$, find the complex number corresponding to vector $\overrightarrow{OB}$.  
$(2)$ If point $B$ from $(1)$ is symmetric to the imaginary axis at point $C$, find the complex number corresponding to point $C$.

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