
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

Filomena has a mobile phone with the following arrangement of buttons:

| 1 | 2 | 3 |
| :---: | :---: | :---: |
| 4 | 5 | 6 |
| 7 | 8 | 9 |
| 0 |   |   |
|   |   |   |
|   |   |   |

Her best friend Kunhuta's nine-digit phone number has the following properties:

- All digits in Kunhuta's phone number are unique.
- The first four digits are sorted in ascending order and the centers of their buttons form a square.
- The centers of the buttons of the last four digits also form a square.
- The phone number is divisible by three and five.

How many different nine-digit numbers could potentially be Kunhuta's phone number?

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