
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
The faces of a cube are labeled with six distinct natural numbers from 6 to 11. The cube is rolled twice. The first time, the sum of the numbers on the four lateral faces is 36, and the second time, the sum is 33. What number is written on the face opposite to the face with the number 10? Justify your answer.

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