
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 bag contains $6$ balls, $4$ of which are labeled $1$ and $2$ are labeled $2$. The probability of drawing any ball is the same. Now, person A draws two balls from the bag, and the sum of the numbers on the two balls is $m$. Person A then puts the balls back in the bag, and person B draws two balls, recording the sum of the numbers on the two balls as $n$. Find the probability that $m < n$.

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