
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, 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 \(E\) and \(F\), with \(E\) on the same side of line \(CD\) as \(A\).

Provide a simple equivalent condition (expressed in the side lengths and/or angles of the trapezoid) for the angles \( \angle BSE \) and \( \angle FSC \) to be 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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