
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
Petya marked 5 points on one face of a cube, then turned the cube and marked 6 points on the adjacent face, then turned again and marked 7 points on the next face, and so on. He marked points on each face. What is the maximum number of points that can be on two opposite faces combined?

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