
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
The casino offers a game under the following rules. A player bets any whole number of dollars (but no more than they currently have) either on heads or tails. Then a coin is flipped. If the player guesses correctly, they get back their bet plus the same amount of money in addition. If they guess incorrectly, 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 how the coin lands. Joe came 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 take away from the casino after such a game?

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