
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 semicircle with diameter \( AB \) and center at point \( O \) is divided by points \( C \) and \( D \) into three parts such that point \( C \) lies on arc \( AD \). From point \( D \), perpendiculars \( DE \) and \( DF \) are drawn to segments \( OC \) and \( AB \) respectively. It turns out that \( DE \) is the angle bisector of triangle \( ADC \), and \( DO \) is the angle bisector of triangle \( ADF \). Find the angle \( CAD \).

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