
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 right triangle $ABC$, where $AB = BC$, point $D$ is the midpoint of $\overline{BC}$. Point $E$ is on the extension of $\overline{AC}$ such that $CE = 15$ units. If $D$ is also the midpoint of $\overline{AE}$, what is the length of $\overline{BD}$? Express your answer as a decimal to the nearest tenth.

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