
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 \( ABCD \) be a convex trapezoid such that \( \angle DAB = \angle ABC = 90^\circ \), \( DA = 2 \), \( AB = 3 \), and \( BC = 8 \). Let \( \omega \) be a circle passing through \( A \) and tangent to segment \( \overline{CD} \) at point \( T \). Suppose that the center of \( \omega \) lies on line \( BC \). Compute \( CT \).

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