
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
The vertices \(B, C, D\) of quadrilateral \(ABCD\) are located on a circle with center \(O\). This circle intersects side \(AD\) at point \(E\) and side \(AB\) at point \(F\). It is known that the chords \(BF\), \(FE\), and \(ED\) are equal, and the chords \(BC\) and \(CD\) are also equal to each other. Find the angle \(OBC\), given that angle \(DAB\) is a right angle.

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