
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
Justine has two fair dice, one with sides labeled  $1,2,\ldots, m$  and one with sides labeled  $1,2,\ldots, n.$  She rolls both dice once. If  $\tfrac{3}{20}$  is the probability that at least one of the numbers showing is at most 3, find the sum of all distinct possible values of  $m+n$ .

*Proposed by Justin Stevens*

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