
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
There are four balls in a bag, which are identical in shape and size. The balls are numbered $1$, $2$, $3$, and $4$ respectively.
(i) Calculate the probability that the product of the numbers of two randomly drawn balls from the bag is not greater than $4$.
(ii) Randomly draw a ball from the bag, its number is $m$, put the ball back into the bag, and then draw another ball from the bag, its number is $n$. Calculate the probability that $|n-m|<2$.

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