
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
Segment  $AB$  of length  $13$  is the diameter of a semicircle. Points  $C$  and  $D$  are located on the semicircle but not on segment  $AB$ . Segments  $AC$  and  $BD$  both have length  $5$ . Given that the length of  $CD$  can be expressed as  $\frac{a}{b}$  where  $a$  and  $b$  are relatively prime positive integers, find  $a +b$ .


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