
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  $ABC$  be a triangle with  $\angle A = 60^\circ$ ,  $AB = 12$ ,  $AC = 14$ . Point  $D$  is on  $BC$  such that  $\angle BAD = \angle CAD$ . Extend  $AD$  to meet the circumcircle at  $M$ . The circumcircle of  $BDM$  intersects  $AB$  at  $K \neq B$ , and line  $KM$  intersects the circumcircle of  $CDM$  at  $L \neq M$ . Find  $\frac{KM}{LM}$ .

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