
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
In a bag, there are four balls that are identical in shape and size, but each ball is numbered differently as 1, 2, 3, or 4.
(1) If two balls are randomly drawn from the bag, what is the probability that the sum of the numbers on these balls does not exceed 4?
(2) If one ball is randomly drawn from the bag and its number is denoted as $m$, after which the ball is put back in the bag, and then a second ball is drawn with its number denoted as $n$, what is the probability that $n < m + 2$?

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