
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
In the isosceles trapezoid \(ABCD\), a circle is inscribed, touching the sides of the trapezoid at points \(T_1, T_2, T_3, T_4\). Let \(K\) be the intersection point of \(CT_3\) and \(T_1T_2\). In what ratio does point \(K\) divide \(T_1T_2\)?

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