
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
Given that $ABC$ is a triangle with $m(\widehat{ABC}) = 90^{\circ}$, the circle with diameter $AB$ intersects the side $[AC]$ at $D$, and the tangent to the circle at $D$ meets $BC$ at $E$ with $|EC| =2$, find $|AC|^2 - |AE|^2$.

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