
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 $\triangle ABC, \overline{CA} = \overline{CB}$. A rhombus $BCDE$ is constructed on segment $BC$ such that $B$ and $C$ are consecutive vertices of the rhombus. If $BD$ is perpendicular to $DE$, and $x$ denotes the measure in degrees of $\angle BAE$ (where $A$ and $E$ are extended to meet at point $E$), then determine $x$.
A) 90°
B) 45°
C) 22.5°
D) 30°
E) 11.25°

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