
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 $\triangle BAD$, which is right-angled at $B$, point $C$ is positioned on line segment $AD$ such that $A$ and $D$ are equidistant from $C$ (i.e., $AC = CD$). Moreover, it's known that the length of side $BC$ is twice that of side $AB$ (i.e., $BC = 2AB$). Determine the magnitude of $\angle DAB$.
A) $22.5^\circ$
B) $30^\circ$
C) $45^\circ$
D) $60^\circ$
E) $67.5^\circ$

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