
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
Given Mr. A owns a home worth $500,000, determine the final net gain or loss for Mr. A, after selling the house to Mr. B at a 15% profit, having Mr. B sell it back at a 5% loss, having Mr. A sell it again at a 10% profit, and having Mr. B sell it back again at a 10% loss.

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