
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 four-digit number is called delightful if: 
1. It is divisible by 25,
2. The sum of its digits is divisible by 25,
3. The product of its digits is divisible by 25. 

Find all delightful numbers.

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