
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 computer generates all pairs of real numbers  $x, y \in (0, 1)$  for which the numbers  $a = x+my$  and  $b = y+mx$  are both integers, where  $m$  is a given positive integer. Finding one such pair  $(x, y)$  takes  $5$  seconds. Find  $m$  if  the computer needs  $595$  seconds to find all possible ordered pairs  $(x, y)$ .

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