
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
Triangle $ABC$ is a right isosceles triangle with $AB = BC$. Point $D$ is the midpoint of $\overline{BC}$ and point $E$ is on extension of $\overline{AC}$ such that $DE = 15$ units is the perpendicular bisector of $\overline{AC}$. What is the length of $\overline{BD}$?

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