
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
Around the vertex of an isosceles triangle, we draw a circle $k$ with an arbitrary radius, and from the endpoints of the base, we draw tangents to $k$. What is the geometric locus of all the intersection points of the four tangents, if the radius of $k$ can assume any possible value?

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