
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 parallelogram \(ABCD\), side \(AD\) is equal to 6. The angle bisector of \(\angle ADC\) intersects line \(AB\) at point \(E\). In triangle \(ADE\), an inscribed circle touches side \(AE\) at point \(K\) and side \(AD\) at point \(T\). Given that \(KT = 3\), find the angle \(\angle BAD\).

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