
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 $n!!$ similarly as in the original problem. Calculate the sum $\sum_{i=1}^{11} \frac{(2i-1)!!}{(2i)!!}$ and when expressed as a fraction in lowest terms, find its denominator in the form $2^a b$ where $b$ is odd. Find $\frac{ab}{10}$.

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