
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
If complex numbers \(z_{1}, z_{2}, z_{3}\) satisfy \(\frac{z_{3}-z_{1}}{z_{2}-z_{1}}=a i \ (a \in \mathbf{R}, a \neq 0)\), then the angle between the vectors \(\overrightarrow{Z_{1} Z_{2}}\) and \(\overrightarrow{Z_{1} Z_{3}}\) is \(\qquad\).

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