
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
On a fair cube with six faces, three of the faces are labeled with the number 0, two faces are labeled with the number 1, and one face is labeled with the number 2. When the cube is rolled twice, what is the mathematical expectation of the product of the numbers on the top faces?

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