
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
$ABC$ is an isosceles right triangle. On the extension of the hypotenuse $AB$ beyond point $A$, point $D$ is taken such that $AB = 2AD$. Points $M$ and $N$ on the side $AC$ are such that $AM = NC$. On the extension of the side $CB$ beyond point $B$, point $K$ is taken such that $CN = BK$. Find the angle between the lines $NK$ and $DM$.

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