
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
In the process of learning numbers, we are always curious about some numbers with certain characteristics, such as when learning natural numbers, we discover a special kind of natural number - "good number".  
Definition: For a three-digit natural number *n*, where each digit is not 0, and the sum of the hundreds digit and the tens digit is exactly divisible by the units digit, then this natural number *n* is called a "good number".  
For example: 426 is a "good number" because 4, 2, and 6 are all not 0, and 4 + 2 = 6, and 6 is divisible by 6;  
643 is not a "good number" because 6 + 4 = 10, and 10 is not divisible by 3.  
(1) Determine if 312 and 675 are "good numbers"? Explain your reasoning.  
(2) Find the number of all "good numbers" where the hundreds digit is 5 greater than the tens digit, and explain your reasoning.

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