
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  $\Delta ABC$ ,  $AC=kAB$ , with  $k>1$ . The internal angle bisector of  $\angle BAC$  meets  $BC$  at  $D$ . The circle with  $AC$  as diameter cuts the extension of  $AD$  at  $E$ . Express  $\dfrac{AD}{AE}$  in terms of  $k$ .

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