
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
Calculate the expected value of the product of the numbers facing up when a fair cube, with three faces labeled 0, two faces labeled 1, and one face labeled 2, is thrown twice.

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