
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 die, 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" faces (excluding the bottom and top faces) was 33, and the second time the sum was 35. What number can be on the face opposite the face with the number 7? Find all possible options.

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