
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
In a set of $12$ coins consisting of $9$ identical genuine coins and $3$ counterfeit coins of the same weight but different from the genuine coins, three pairs of coins are selected sequentially without replacement. If the total weight of the first pair equals the total weight of the second pair and also equals the total weight of the third pair, what is the probability that all six selected coins are genuine?
A) $\frac{1}{11}$
B) $\frac{45}{528}$
C) $\frac{90}{528}$
D) $\frac{210}{2310}$
E) $1$

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