
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 $\$12,000$ and a house initially valued at $\$12,000$. Mr. B starts with $\$13,000$. Mr. A sells the house to Mr. B for $\$14,000$, then Mr. B sells the house back to Mr. A for $\$11,000$, and finally, Mr. A sells the house again to Mr. B for $\$15,000$. Calculate the final cash amounts for Mr. A and Mr. B.

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