
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
A seven-digit natural number \( N \) is called interesting if:

- It consists of non-zero digits;
- It is divisible by 4;
- Any number obtained from \( N \) by permuting its digits is also divisible by 4.

How many interesting numbers exist?

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