
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 a triangle with sides  $AB = 6$ ,  $BC = 10$ , and  $CA = 8$ . Let  $M$  and  $N$  be the midpoints of  $BA$  and  $BC$ , respectively. Choose the point  $Y$  on ray  $CM$  so that the circumcircle of triangle  $AMY$  is tangent to  $AN$ . Find the area of triangle  $NAY$ .

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