
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 $ABC$ with $\angle B = 90^\circ$, $AB = 6$ units, and $AC = 8$ units. Point $D$ is the midpoint of both $\overline{BC}$ and $\overline{AE}$. If $\overline{CE}$ is 10 units long, find the length of $\overline{BD}$.

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