
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 circle with center  $O$  has radius  $5,$  and has two points  $A,B$  on the circle such that  $\angle AOB = 90^{\circ}.$  Rays  $OA$  and  $OB$  are extended to points  $C$  and  $D,$  respectively, such that  $AB$  is parallel to  $CD,$  and the length of  $CD$  is  $200\%$  more than the radius of circle  $O.$  Determine the length of  $AC.$ 

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