
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 angle bisector \(\overline{AT}\) intersects \(\overline{DE}\) at \(F.\)  If \(AD = 2,\) \(DB = 2,\) \(AE = 3,\) and \(EC = 3,\) compute \(\frac{AF}{AT}.\)

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