
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
Given two non-negative integers  $m>n$ , let's say that  $m$  *ends in*  $n$  if we can get  $n$  by erasing some digits (from left to right) in the decimal representation of  $m$ . For example, 329 ends in 29, and also in 9.

Determine how many three-digit numbers end in the product of their digits.

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