
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
Calculate:<br/>$(1)(3+2i)+(\sqrt{3}-2)i$;<br/>$(2)\frac{9+2i}{2+i}$;<br/>$(3)\frac{(-1+i)(2+i)}{{i}^{3}}$;<br/>$(4)$Given vectors $\overrightarrow{a}=(-1,2)$ and $\overrightarrow{b}=(2,1)$, calculate $2\overrightarrow{a}+3\overrightarrow{b}$ and $\overrightarrow{a}•\overrightarrow{b}$;<br/>$(5)$Given vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ satisfy $|\overrightarrow{a}|=1$ and $\overrightarrow{a}•\overrightarrow{b}=-1$, calculate $\overrightarrow{a}•(2\overrightarrow{a}-\overrightarrow{b})$.

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