
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
In the triangle \(ABC\), a circle passes through the point \(A\), the midpoint \(E\) of \(AC\), the midpoint \(F\) of \(AB\), and is tangent to the side \(BC\) at \(D\). Suppose
\[ \frac{AB}{AC} + \frac{AC}{AB} = 4. \]
Determine the size of \(\angle EDF\) in degrees.

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