
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
Let $X = \left\{\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5},\frac{1}{6}\right\}$. For a subset $G \subseteq X$, define the "product" of $G$ as the product of all elements in $G$ (the "product" of a singleton set is the element itself). Then, the sum of the "products" of all non-empty subsets of $X$ is \_\_\_\_\_\_.

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