
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 $S_n = \{1, 2, 3, \ldots, n\}$. If $X \subseteq S_n$, the product of all elements in $X$ is called the capacity of $X$ (if $X$ contains only one element, then the value of that element is its capacity, and the capacity of the empty set is defined as 0). If the capacity of $X$ is odd (even), then $X$ is called an odd (even) subset of $S_n$. If $n=4$, the sum of the capacities of all even subsets of $S_n$ is $\boxed{\text{\_\_\_\_\_\_\_\_\_\_\_\_}}$.

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