
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
Quadrilateral  $ABCD$  is cyclic with  $AB = CD = 6$ . Given that  $AC = BD = 8$  and  $AD+3 = BC$ , the area of  $ABCD$  can be written in the form  $\frac{p\sqrt{q}}{r}$ , where  $p, q$ , and  $ r$  are positive integers such that  $p$  and  $ r$  are relatively prime and that  $q$  is square-free. Compute  $p + q + r$ .

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