
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
 $4.$  Harry, Hermione, and Ron go to Diagon Alley to buy chocolate frogs. If Harry and Hermione spent one-fourth of their own money, they would spend  $3$  galleons in total. If Harry and Ron spent one-fifth of their own money, they would spend  $24$  galleons in total. Everyone has a whole number of galleons, and the number of galleons between the three of them is  a multiple of  $7$ . What are all the possible number of galleons that Harry can have?

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