
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 $\triangle ABC$, $\angle A = 60^\circ$ and $\angle B = 45^\circ$. A line $DE$, with $D$ on $AB$ and $E$ originally thought to be on $AC$, forms $\angle ADE = 75^\circ$. The line divides $\triangle ABC$ into two regions of equal area. Determine the ratio $\frac{AD}{AB}$.
A) $\frac{1}{3}$
B) $\frac{1}{2}$
C) $\frac{2}{3}$
D) $\frac{3}{4}$
E) $\frac{1}{4}$

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