
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
Two circles centered at  $O$  and  $P$  have radii of length  $5$  and  $6$  respectively. Circle  $O$  passes through point  $P$ . Let the intersection points of circles  $O$  and  $P$  be  $M$  and  $N$ . The area of triangle  $\vartriangle MNP$  can be written in simplest form as  $a/b$ . Find  $a + b$ .

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