
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
Each integer $1$ through $9$ is written on a separate slip of paper and all nine slips are put into a hat. If Jack and Jill pick one slip at random and put it back each time, calculate the probability that the units digit of the sum of their integers is each digit from 0 to 9.

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