
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 the circles  $k_1$  and  $k_2$  intersect at two points  $A$  and  $B$ , and let  $t$  be a common tangent of  $k_1$  and  $k_2$  that touches  $k_1$  and  $k_2$  at  $M$  and  $N$  respectively. If  $t\perp AM$  and  $MN=2AM$ , evaluate the angle  $NMB$ .

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