
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 card with the digit 5, two cards with the digit 3, and one hundred cards with the digit 2. 
a) In how many ways can a ten-digit number be formed from these cards such that the product of the digits ends in 0?

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

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