
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
There is one piece of paper with the digit 5, two pieces of paper with the digit 3, and one hundred pieces of paper with the digit 2.

a) In how many ways can a ten-digit number be formed such that the product of its digits ends in 0?

b) All such numbers were written in ascending order. What number is in the 455th position?

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