
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 \( z_{1}, z_{2}, z_{3} \) satisfy \( \frac{z_{3}-z_{1}}{z_{2}-z_{1}} = a \mathrm{i} \) where \( a \) is a non-zero real number (\( a \in \mathbf{R}, a \neq 0 \)), find the angle between the vectors \( \overrightarrow{Z_{1} Z_{2}} \) and \( \overrightarrow{Z_{1} Z_{3}} \).

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