
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
How many natural numbers \( \mathrm{N} \) greater than 300 exist such that exactly two out of the numbers \( 4 \mathrm{~N}, \mathrm{~N} - 300, \mathrm{N} + 45, 2\mathrm{N} \) are four-digit numbers?

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