
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
A kite is inscribed in a circle with center  $O$  and radius  $60$ . The diagonals of the kite meet at a point  $P$ , and  $OP$  is an integer. The minimum possible area of the kite can be expressed in the form  $a\sqrt{b}$ , where  $a$  and  $b$  are positive integers and  $b$  is squarefree. Find  $a+b$ .

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