
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
Isosceles trapezoid  $ ABCD$ , with  $ AB \parallel CD$ , is such that there exists a circle  $ \Gamma$  tangent to its four sides. Let  $ T \equal{} \Gamma \cap BC$ , and  $ P \equal{} \Gamma \cap AT$  ( $ P \neq T$ ).
If  $ \frac{AP}{AT} \equal{} \frac{2}{5}$ , compute  $ \frac{AB}{CD}$ .

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