
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
Define $n!!$ as previously, for $n$ odd it is $n(n-2)(n-4)\cdots 3\cdot 1$ and for $n$ even it is $n(n-2)(n-4)\cdots 4\cdot 2$. Calculate $\sum_{i=1}^{12} \frac{(2i-1)!!}{(2i)!!}$ and express this sum as a fraction in its lowest terms. Let the denominator be $2^cd$ where $d$ is odd. Find $\dfrac{cd}{10}$.

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