
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
Two robbers stole 300 gold coins. They decided to divide them as follows: the first robber puts some coins (possibly all) in a bag, and the second robber decides who will get the bag; then the process is repeated several more times. The division ends when

- either all the money has been used up,
- or one of them has received 11 bags - in which case all the remaining money immediately goes to the other robber.

What is the maximum number of coins that the first robber can be guaranteed to get?

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