
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 uniform cube dice with numbers 1, 2, 3, 4, 5, 6 marked on its faces is thrown twice. The sum of the numbers on the top faces of the two dice is defined as the score of that throw. The probability that the score is divisible by 4 with a remainder of 2 when throwing the dice is \_\_\_\_\_\_.

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