
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
David, when submitting a problem for CMIMC, wrote his answer as  $100\tfrac xy$ , where  $x$  and  $y$  are two positive integers with  $x<y$ . Andrew interpreted the expression as a product of two rational numbers, while Patrick interpreted the answer as a mixed fraction. In this case, Patrick's number was exactly double Andrew's!  What is the smallest possible value of  $x+y$ ?

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