
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
Alex launches his boat into a river and heads upstream at a constant speed. At the same time at a point  $8$  miles upstream from Alex, Alice launches her boat and heads downstream at a constant speed. Both boats move at  $6$  miles per hour in still water, but the river is  owing downstream at  $2\frac{3}{10}$  miles per hour. Alex and Alice will meet at a point that is  $\frac{m}{n}$  miles from Alex's starting point, where  $m$  and  $n$  are relatively prime positive integers. Find  $m + n$ .

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