
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 the measure of base $\overline{AB}$ is three times the measure of the base $\overline{CD}$. Additionally, the perimeter of trapezoid $ABCD$ is 36 units. Point $E$ is the intersection of the diagonals. If the length of diagonal $\overline{AC}$ is 18 units, determine the length of segment $\overline{EC}$.

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