
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 $\triangle ABC$, given that $AC - AB = \frac{\sqrt{2}}{2} BC$. Point $D$ is within the triangle $\triangle ABC$ such that $AD = AB$. A perpendicular line is drawn from $D$ to $BC$, intersecting at point $E$. Given that $3BE = CE$, find the measure of $\angle ADE$.

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