
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 quadrilateral \(ABCD\) with perpendicular diagonals is inscribed in a circle.

Perpendiculars dropped from vertices \(B\) and \(C\) to side \(AD\) intersect the diagonals \(AC\) and \(BD\) at points \(E\) and \(F\) respectively. Find \(EF\), given that \(BC = 1\).

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