
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 that Michael ordered $6$ pairs of black socks and some number of pairs of blue socks, where the price of a pair of black socks was three times that of a pair of blue socks, and due to a mistake, the quantities of black and blue socks were interchanged, resulting in a 60% increase in the total cost of the order, find the ratio of the number of pairs of black socks to the number of pairs of blue socks in the original order.

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