
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
Given circles $⊙C_{1} : (x-2)^{2}+(y-2)^{2}= r_{1}^{2} (r_{1}>0)$ and $⊙C_{2} : (x+1)^{2}+(y+1)^{2}= r_{2}^{2} (r_{2}>0)$, where $⊙C_{1}$ and $⊙C_{2}$ are tangent to each other. One of their external common tangent lines has a slope of 7. Determine the value of $r_{1}r_{2}$.

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