
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  $\Omega_1$  and  $\Omega_2$  be two circles in the plane.  Suppose the common external tangent to  $\Omega_1$  and  $\Omega_2$  has length  $2017$  while their common internal tangent has length  $2009$ .  Find the product of the radii of  $\Omega_1$  and  $\Omega_2$ .

*Proposed by David Altizio*

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