
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, B, and C each participate in a cycle of transactions. Initially:
- A gives $B$ as many cents as $B$ has, and $C$, as many cents as $C$ has.
- B then gives $A$ as many cents as $A$ has, and $C$ as many cents as $C$ has.
- C finally gives $A$ as many cents as $A$ has, and $B$ as many cents as $B$ has.
After all transactions, each has 128 cents. What is the initial amount of money that A had?

The total money remains constant throughout the transactions.
**A)** 72
**B)** 80
**C)** 88
**D)** 98

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