
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
Consider triangle \(ABC\) with \(\angle A = 2 \angle B\). The angle bisectors from \(A\) and \(C\) intersect at \(D\), and the angle bisector from \(C\) intersects \(\overline{AB}\) at \(E\). If \(\frac{DE}{DC} = \frac{1}{3}\), compute \(\frac{AB}{AC}\).

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