
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 lock on a safe consists of three wheels, each of which may be set in eight different positions. Due to a defect in the safe mechanism, the door will open if any two of the three wheels are in the correct position. What is the smallest number of combinations that must be tried to guarantee being able to open the safe (assuming that the "right combination" is not known)?

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