
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
Given the numbers  $ 1,2,2^2, \ldots ,2^{n\minus{}1}$ , for a specific permutation  $ \sigma \equal{} x_1,x_2, \ldots, x_n$  of these numbers we define  $ S_1(\sigma) \equal{} x_1$ ,  $ S_2(\sigma)\equal{}x_1\plus{}x_2$ ,  $ \ldots$  and  $ Q(\sigma)\equal{}S_1(\sigma)S_2(\sigma)\cdot \cdot \cdot S_n(\sigma)$ . Evaluate  $ \sum 1/Q(\sigma)$ , where the sum is taken over all possible permutations.

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