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

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

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