
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!!$  to be  $ n(n\minus{}2)(n\minus{}4)\ldots3\cdot1$  for  $ n$  odd and  $ n(n\minus{}2)(n\minus{}4)\ldots4\cdot2$  for  $ n$  even. When  $ \displaystyle \sum_{i\equal{}1}^{2009} \frac{(2i\minus{}1)!!}{(2i)!!}$  is expressed as a fraction in lowest terms, its denominator is  $ 2^ab$  with  $ b$  odd. Find  $ \displaystyle \frac{ab}{10}$ .

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