
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 worth $\textdollar{15000}$, while Mr. $B$ starts with $\textdollar{20000}$. The house is sold to Mr. $B$ for $\textdollar{18000}$, then sold back to Mr. $A$ for $\textdollar{12000}$, and finally sold back to Mr. $B$ for $\textdollar{16000}$. Calculate the final cash and house ownership for both Mr. $A$ and Mr. $B$, and determine the net change in their wealth.

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