
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
On the sides  $AB$  and  $BC$  of triangle  $ABC$ , points  $K$  and  $M$  are chosen such that the quadrilaterals  $AKMC$  and  $KBMN$  are cyclic , where  $N = AM \cap CK$  . If these quads have the same circumradii, find  $\angle ABC$ 

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