
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 the faces of a six-sided die, the numbers $6, 7, 8, 9, 10, 11$ are written. The die was rolled twice. The first time, the sum of the numbers on the four "vertical" (i.e., excluding the bottom and top) faces was $33$, and the second time it was $35$. What number can be written on the face opposite the face with the number $7$? Find all possible options.

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