
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 two points: \( A_{1}(x_{1}, y_{1}, z_{1}) \) and \( A_{2}(x_{2}, y_{2}, z_{2}) \). The point \( P \) defines two vectors: \( \overrightarrow{P A}_{1}=\vec{q}_{1} \) and \( \overrightarrow{P A}_{2}=\vec{q}_{2} \). What is the set of points \( P \) for which the condition \( \vec{q}_{1} \cdot \vec{q}_{2}=0 \) holds?

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