
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
If digits in different positions are considered different, then in a base-$d$ numbering system, $nd$ digits allow writing $d^n$ numbers (from 0 to $d^n-1$). Which numbering system is the most economical in this respect, i.e., allows writing the most significant number of numbers using a given number of digits? (When comparing numbering systems with bases $d_1$ and $d_2$, we only consider sets of $m$ digits, where $m$ is divisible by both $d_1$ and $d_2$.)

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