
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
Jonathan has a magical coin machine which takes coins in amounts of  $7, 8$ , and  $9$ . If he puts in  $7$  coins, he gets  $3$  coins back; if he puts in  $8$ , he gets  $11$  back; and if he puts in  $9$ , he gets  $4$  back. The coin machine does not allow two entries of the same amount to happen consecutively. Starting with  $15$  coins, what is the minimum number of entries he can make to end up with  $4$  coins?

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