
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
There are circles \(\omega_1\) and \(\omega_2\). They intersect in two points, one of which is the point \(A\). \(B\) lies on \(\omega_1\) such that \(AB\) is tangent to \(\omega_2\). The tangent to \(\omega_1\) at \(B\) intersects \(\omega_2\) at \(C\) and \(D\), where \(D\) is closer to \(B\). \(AD\) intersects \(\omega_1\) again at \(E\). If \(BD = 3\) and \(CD = 13\), find \(\frac{EB}{ED}\).

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