
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 distinct points \( A \) and \( B \), find the locus of points \( M \) in the plane such that \( \overrightarrow{M A} \cdot \overrightarrow{M B} = k^{2} \) (where \( k \) is a non-zero real constant).

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