
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, and let  $BCDE$ ,  $CAFG$ ,  $ABHI$  be squares that do not overlap the triangle with centers  $X$ ,  $Y$ ,  $Z$  respectively. Given that  $AX=6$ ,  $BY=7$ , and  $CA=8$ , find the area of triangle  $XYZ$ .

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