
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
John ordered $6$ pairs of black socks and some additional pairs of blue socks. The price of the black socks per pair was twice that of the blue. When the order was filled, it was found that the number of pairs of the two colors had been interchanged, increasing the bill by $60\%$. Determine the ratio of the number of pairs of black socks to the number of pairs of blue socks in the original order.
A) $\frac{1}{5}$
B) $\frac{2}{11}$
C) $\frac{1}{6}$
D) $\frac{3}{17}$
E) $\frac{1}{7}$

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