
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 a $\Sigma(\alpha)$ system and a line intersecting the axes, rotate the $\Sigma(\alpha)$ system around the intersection point of the axes. Determine the point in every position of the system whose adjoint line is the intersecting line. What is the locus of these points?

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