
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. During a series of 4 rounds, they bet each time one-third of the amount they have. They win twice and lose twice, but now the wins are twice the staked amount, and losses mean losing the staked amount. Determine the final amount of money the gambler has, assuming the wins and losses happen in an arbitrary fixed order.
A) $\frac{8000}{81}$
B) $\frac{5000}{81}$
C) $\frac{7500}{81}$
D) $\frac{7200}{81}$

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