
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 house worth $12000 is sold by Mr. A to Mr. B at a 10% loss. Mr. B sells the house back to Mr. A at a 15% gain.
**A)** Mr. A loses $402$  
**B)** Mr. A loses $420$  
**C)** Mr. A loses $12420$  
**D)** Mr. A regains the house at no cost

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