
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 triangle \( ABC \), points \( D \) and \( E \) are on \( \overline{AB} \) and \( \overline{AC} \), respectively, and the angle bisector \( \overline{AT} \) intersects \( \overline{DE} \) at \( F \). If \( AD = 2, \) \( DB = 6, \) \( AE = 5, \) and \( EC = 3, \) compute \( \frac{AF}{AT} \).

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