
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
Ali Baba and a thief are sharing a treasure consisting of 100 gold coins, divided into 10 piles of 10 coins each. Ali Baba selects 4 piles, places a cup near each of them, and puts some coins (at least one, but not the whole pile) into each cup. The thief then rearranges the cups, changing their initial placements, and the coins are poured out from the cups into the piles where the cups ended up. Ali Baba can then choose 4 piles again, place cups near them, and repeat the process. At any point, Ali Baba can leave, taking any three piles of his choice with him. The remaining coins go to the thief. What is the maximum number of coins Ali Baba can take, given that the thief also tries to maximize his own gain?

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