
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
Three counterfeit coins, each heavier than $10$ identical genuine coins, are mixed together making a total of $13$ coins. A pair of coins is selected randomly without replacement from the $13$ coins followed by another pair from the remaining $11$ coins. The combined weight of the first pair is less than the combined weight of the second pair. What is the probability that all four selected coins are genuine?
A) $\frac{14}{23}$
B) $\frac{55}{143}$
C) $\frac{2}{3}$
D) $\frac{5}{6}$
E) $\frac{1}{2}$

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