
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
Let the vertices $B$ and $C$ of a triangle be fixed, and let the vertex $A$ move such that the Brocard angle $\varphi$ of the triangle $ABC$ remains constant. Then the point $A$ moves along a circle of radius $\frac{a}{2} \sqrt{\operatorname{ctg}^{2} \varphi - 3}$, where $a = BC$ (Neuberg circle).

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