
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
Mr. $A$ starts with $\textdollar{15000}$ and a house valued at $\textdollar{12000}$. Mr. $B$ starts with $\textdollar{13000}$. Mr. $A$ sells the house to Mr. $B$ for $\textdollar{14000}$. After a while, Mr. $B$ sells the house back to Mr. $A$ for $\textdollar{10000}$. Calculate the final amount of cash and analyze the change in the net worth for both Mr. $A$ and Mr. $B$.
A) Mr. A gains $\textdollar{3000}$, Mr. B loses $\textdollar{3000}$
B) Mr. A gains $\textdollar{4000}$, Mr. B loses $\textdollar{4000}$
C) Mr. A gains $\textdollar{5000}$, Mr. B loses $\textdollar{5000}$
D) No net change for either Mr. A or Mr. B

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