
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
Malmer Pebane's apartment uses a six-digit access code, with leading zeros allowed. He noticed that his fingers leave  that reveal which digits were pressed. He decided to change his access code to provide the largest number of possible combinations for a burglar to try when the digits are known. For each number of distinct digits that could be used in the access code, calculate the number of possible combinations when the digits are known but their order and frequency are not known. For example, if there are smudges on  $3$  and  $9,$  two possible codes are  $393939$  and  $993999.$  Which number of distinct digits in the access code offers the most combinations?

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