
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 person starts with $100 and makes 5 bets, winning three times and losing twice, with one unique rule that if the first bet is a loss, it nullifies one win's effect. Each wager is for half the money remaining at the time of the bet. Assuming each win and loss occur with equal probability, calculate the final amount of money the person has.

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