
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 three-digit number $N$ is modified by subtracting 3, adding 4, dividing by 5, and multiplying by 6, resulting in four integers. It is known that the sum of the digits of these four integers are exactly four consecutive natural numbers. Find the number of three-digit numbers $N$ that satisfy this condition.

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