
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
Six pirates - a captain and five crew members - are sitting around a campfire facing the center. They need to divide a treasure of 180 gold coins. The captain proposes a way to divide the coins (i.e., how many coins each pirate should receive: each pirate must receive a whole non-negative number of coins; different pirates may receive different amounts of coins). After this, the other five pirates vote on the captain's proposal. A pirate will vote "yes" only if he receives more coins than each of his two neighbors. The proposal is accepted if at least three out of the five crew members vote "yes".

What is the maximum number of coins the captain can receive under these rules?

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