
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
$ABCD$ is a trapezoid where $\overline{AB}$ is three times the length of $\overline{CD}$, and the height from $D$ to line $AB$ is 5 units. Point $E$ is the intersection of the diagonals. If the length of diagonal $\overline{AC}$ is 15, find the length of segment $\overline{EC}$. Express your answer as a common fraction.

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