
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
(4 points) (2015•Yangpu District Mock Test) For every non-empty subset of the natural number set $N^*$, we define the "alternating sum" as follows: arrange the elements of the subset in descending order, then start from the largest number and alternately add and subtract each number. For example, the alternating sum of $\{1, 2, 4, 6, 9\}$ is $9 - 6 + 4 - 2 + 1 = 6$; then, the total sum of the alternating sums of all non-empty subsets of the set $\{1, 2, 3, 4, 5, 6, 7\}$ is.

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