
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
Alice picks a number uniformly at random from the first  $5$  even positive integers, and Palice picks a number uniformly at random from the first  $5$  odd positive integers. If Alice picks a larger number than Palice with probability  $\frac{m}{n}$  for relatively prime positive integers  $m,n$ , compute  $m+n$ .

*2020 CCA Math Bonanza Lightning Round #4.1*

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