
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 $\triangle ABC$, $∠ABC=\frac{π}{2}$, points $D$ and $E$ lie on side $BC$, $\angle BAD=\angle DAE=\angle EAC$, $BD=3$, and $DE=5$. Find:<br/>
$(1)$ $AB$;<br/>
$(2)$ the area of $\triangle AEC$.

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