
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  $O_1$  and  $O_2$  intersect at points  $A$  and  $B$ . Lines  $\overline{AC}$  and  $\overline{BD}$  are drawn such that  $C$  is on  $O_1$  and  $D$  is on  $O_2$  and  $\overline{AC} \perp \overline{AB}$  and  $\overline{BD} \perp \overline{AB}$ . If minor arc  $AB= 45$  degrees relative to  $O_1$  and minor arc  $AB= 60$  degrees relative to  $O_2$  and the radius of  $O_2 = 10$ , the area of quadrilateral  $CADB$  can be expressed in simplest form as  $a + b\sqrt{k} + c\sqrt{\ell}$ . Compute  $a + b + c + k +\ell$ .

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