
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
In a modified version of the game "Money Bag Madness," participants select a sack from a set of 30, each containing different amounts of money from $0.50 to $2,000,000, doubling each amount going from one sack to the next. The sacks contain the following amounts consecutively: $0.50, $1, $2, $4, $8, $16, $32, $64, $128, $256, $512, $1024, $2048, $4096, $8192, $16384, $32768, $65536, $131072, $262144, $524288, $1048576, $2097152. If a participant wants to ensure at least a $40%$ chance of holding a sack containing at least $65536$, how many sacks must they eliminate?

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