
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
Grandpa forgot the four-digit code to his mobile phone. He remembered only that the first digit was not zero, that the middle two digits were either two fours, two sevens, or a four and a seven (in an unknown order), and that the number was divisible by 15. How many possibilities are there for the forgotten code? What digit could be in the first position?

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