
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
In a right-angled coordinate system, two points are given: \( A(-m, 0) \) and \( B(n, 0) \), with \( O(0,0) \) being the origin. Determine the equation for the locus of points from which the line segments \( AO \) and \( OB \) are seen at an equal angle.

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