
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 an acute triangle $ABC$, let $D$ be a point on $[AC]$ and $E$ be a point on $[AB]$ such that $\angle ADB = \angle AEC = 90^{\circ}$. If the perimeter of triangle $AED$ is 9 and the circumradius of $AED$ is $\frac{9}{5}$, and the perimeter of triangle $ABC$ is 15, calculate $|BC|$.

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