
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
The king sent 3 princes to Exotic Island to look for exotic fruits. The eldest prince and the second prince found exotic fruits in a ratio of $2:3$. The third prince did not find any exotic fruits, so he bought some fruits from the eldest prince and the second prince, spending a total of 180 gold coins. After that, all three princes had the same number of exotic fruits. How many gold coins did the third prince give to the second prince?

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