
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
A casino offers a game with the following rules. A player bets any whole number of dollars (but no more than what they have at the moment) either on heads or tails. Then a coin is flipped. If the player guesses correctly, they get their bet back plus the same amount of money. If they guess wrong, the casino takes their bet. If the player loses four times in a row, the casino awards them a consolation win in the next game regardless of the coin's outcome.

Joe comes to the casino with $100. He is committed to making exactly five bets and never betting more than $17. What is the maximum amount of money he can guarantee to leave the casino with after such a game?

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