
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 cube has its six faces numbered such that the sum of the numbers on opposite faces is always 10. Determine the largest sum of three numbers whose faces come together at a corner of the cube.

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