
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 the ﬁgure on the right,  $O$  is the center of the circle,  $OK$  and  $OA$  are perpendicular to one another,  $M$  is the midpoint of  $OK$ ,  $BN$   is parallel to  $OK$ , and  $\angle AMN=\angle NMO$ . Determine the measure of  $\angle A B N$  in degrees.

[asy]
defaultpen(linewidth(0.7)+fontsize(10));
pair O=origin, A=dir(90), K=dir(180), M=0.5*dir(180), N=2/5*dir(90), B=dir(degrees((2/5, sqrt(21/25)))+90);
draw(K--O--A--M--N--B--A^^Circle(origin,1));
label(" $A$ ", A, dir(O--A));
label(" $K$ ", K, dir(O--K));
label(" $B$ ", B, dir(O--B));
label(" $N$ ", N, E);
label(" $M$ ", M, S);
label(" $O$ ", O, SE);[/asy]

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