
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
Triangle \( A B C \) is given in the plane. Let \( A D \) be the angle bisector of \( \angle B A C \); let \( B E \) be the altitude from \( B \) to \( A D \), and let \( F \) be the midpoint of \( A B \). Given that \( A B = 28 \), \( B C = 33 \), and \( C A = 37 \), what is the length of \( E F \)?

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