
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 turbo multiple of a natural number is the smallest multiple of that number composed only of the digits 0 and 1. For example, the turbo multiple of 2, as well as for 5, is 10; the turbo multiple of 3 is 111, and for 110 it is itself.

a) What is the turbo multiple of 20?

b) What is the turbo multiple of 9?

c) What is the turbo multiple of 45?

d) What is the smallest natural number whose turbo multiple is 1110?

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