
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
Consider an amount of $3$ being split into two nonnegative real numbers uniformly at random. Each of the numbers is then rounded to its nearest integer. Calculate the probability that the sum of the two rounded numbers results in $4$.

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