
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 triangle $ABC$ with $\angle A = 45^\circ$, where $BC = 8$, $\overline{BD} \perp \overline{AC}$ with $D$ also being the midpoint of $\overline{AC}$, and $\overline{CE} \perp \overline{AB}$. If $m \angle DBC = 3m \angle ECB$, find the length of segment $EC$.

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