
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  $M$  be the midpoint of the base  $AC$  of an acute-angled isosceles triangle  $ABC$ . Let  $N$  be the reflection of  $M$  in  $BC$ . The line parallel to  $AC$  and passing through  $N$  meets  $AB$  at point  $K$ . Determine the value of  $\angle AKC$ .

(A.Blinkov) 

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