
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
Three dice are rolled. Two of these dice are regular cubic dice with faces numbered from 1 to 6, and the third die has faces numbered with odd numbers only (1, 3, 5, 7, 9, 11). What is the probability that the sum of the numbers shown on the top faces of all three dice is even?

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