
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 such that  $AB = 7$ ,  $BC = 8$ , and  $CA = 9$ . There exists a unique point  $X$  such that  $XB = XC$  and  $XA$  is tangent to the circumcircle of  $ABC$ . If  $XA = \tfrac ab$ , where  $a$  and  $b$  are coprime positive integers, find  $a + b$ .

*Proposed by Alexander Wang*

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