
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
The common external tangent to the circles \(\omega_1\) and \(\omega_2\) touches them at the points \(T_1\) and \(T_2\) respectively. Let \(A\) be an arbitrary point on the extension of the segment \(T_1T_2\) beyond the point \(T_1\) and \(B\) a point on the extension of the segment \(T_1T_2\) beyond the point \(T_2\) such that \(AT_1 = BT_2\). Distinct from a line.

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