
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
We are given a combination lock consisting of 6 rotating discs. Each disc consists of digits $0,1,2, \ldots, 9$, in that order (after digit 9 comes 0). The lock is opened by exactly one combination. A move consists of turning one of the discs one digit in any direction, and the lock opens instantly if the current combination is correct. The discs are initially put in the position 000000, and we know that this combination is not correct.

a) What is the least number of moves necessary to ensure that we have found the correct combination?

b) What is the least number of moves necessary to ensure that we have found the correct combination, if we know that none of the combinations $000000,111111,222222, \ldots, 999999$ is correct?

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