
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 a certain triangle  $ABC$ , there are points  $K$  and  $M$  on sides  $AB$  and  $AC$ , respectively, such that if  $L$  is the intersection of  $MB$  and  $KC$ , then both  $AKLM$  and  $KBCM$  are cyclic quadrilaterals with the same size circumcircles. Find the measures of the interior angles of triangle  $ABC$ .

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