
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
A (convex) trapezoid \(ABCD\) is called "good" if it has a circumcircle, the sides \(AB\) and \(CD\) are the parallel sides, and \(CD\) is shorter than \(AB\). For a good trapezoid \(ABCD\), the following designations are made:

- The line parallel to \(AD\) passing through \(B\) intersects the extension of side \(CD\) at point \(S\).
- The two tangents from \(S\) to the circumcircle of the trapezoid touch it at points \(E\) and \(F\) where \(E\) lies on the same side of line \(CD\) as \(A\).

Give a simple equivalent condition (expressed in terms of the side lengths and/or angles of the trapezoid) for when the two angles \(\angle BSE\) and \(\angle FSC\) are equal in a good trapezoid \(ABCD\).

(Walther Janous)

Answer: The angles \(\angle BSE\) and \(\angle FSC\) are equal if and only if \(\angle BAD = 60^{\circ}\) or \(AB = AD\).

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