
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
Points \( A, B, C, D, E \) are sequentially located on a line such that \( AB = CD = 1 \) and \( BC = DE = 2 \). Circles \( \Omega \) and \( \omega \) are tangent to each other, with \( \Omega \) passing through points \( A \) and \( E \), and \( \omega \) passing through points \( B \) and \( C \). Find the radii of circles \( \Omega \) and \( \omega \) if it is known that their centers and point \( D \) lie on the same line.

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