
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
Let \(ABCD\) be an isosceles trapezoid such that \(AB = 10\), \(BC = 15\), \(CD = 28\), and \(DA = 15\). There is a point \(E\) such that \(\triangle AED\) and \(\triangle AEB\) have the same area and such that \(EC\) is minimal. Find \(EC\).

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