
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
The money of $A$ is in the ratio to the money of $B$ as $8:5$. If $A$ loses $50 \mathrm{~K}$ and $B$ gains $100 \mathrm{~K}$, then their money is in the ratio $5:4$. How much money did each have?

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