
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
Definition: The capacity of a number set is the sum of all elements in the set. For example, the capacity of the number set $\{1, 2, 3\}$ is $1+2+3=6$. Then, the total sum of the capacities of all non-empty sets $A$ that satisfy the condition "If $A \subseteq \{1, 2, 3, 4, 5, 6, 7\}$, and if $a \in A$, then $8-a \in A$" is $\boxed{224}$.

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