
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 an isosceles right-angled triangle. Point  $D$  is chosen on the prolongation of the hypothenuse  $AB$  beyond point  $A$  so that  $AB = 2AD$ . Points  $M$  and  $N$  on side  $AC$  satisfy the relation  $AM = NC$ . Point  $K$  is chosen on the prolongation of  $CB$  beyond point  $B$  so that  $CN = BK$ . Determine the angle between lines  $NK$  and  $DM$ .

(M.Kungozhin) 

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