
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
Two flagpoles with heights of 5 meters and 3 meters stand on a horizontal ground. If the coordinates of the bases of the two flagpoles are determined to be \( A(-5,0) \) and \( B(5,0) \) respectively, find the locus of points on the ground where the angles of elevation to the tops of the poles are equal.

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