
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 small uniform cube has six faces, with three faces labeled 0, two faces labeled 1, and one face labeled 2. The cube is thrown twice. What is the expected value of the product of the numbers on the top faces?

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