
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
An isosceles trapezoid \(ABCD\) with bases \(AB\) and \(CD\) has \(AB=13\), \(CD=17\), and height 3. Let \(E\) be the intersection of \(AC\) and \(BD\). Circles \(\Omega\) and \(\omega\) are circumscribed about triangles \(ABE\) and \(CDE\). Compute the sum of the radii of \(\Omega\) and \(\omega\).

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