
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
(1) Given that $Z$ is a complex number, $Z+2i$, $\frac{Z}{2-i}$ are both real numbers, and the point corresponding to the complex number $((Z+ai)^{2}$ in the complex plane is in the first quadrant, find the range of values for the real number $a$.
(2) Given that the complex numbers corresponding to two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are $z_{1}=3$ and $z_{2}=-5+5i$, find the angle between vectors $\overrightarrow{a}$ and $\overrightarrow{b}$.

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