
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 gambler starts with $100 and makes 4 bets, winning twice and losing twice. The order of wins and losses affects the final amount. The chance for a win is equal to the chance for a loss. If each wager is for half the money remaining at the time of the bet, and each win multiplies the remaining amount by 2, while each loss halves it, determine the final amount if the gambler wins the first and third bets but loses the second and fourth bets.

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