
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 set $M=\{x|1\leq x\leq 8, x\in \mathbb{N}\}$, for its non-empty subset $A$, sum each element $k$ in $A$ after multiplying it by $(-1)^k$ (for example, if $A=\{1,3,6\}$, the sum would be $(-1)^1\cdot1+(-1)^3\cdot3+(-1)^6\cdot6=2$). Then, for all non-empty subsets of $M$, the total sum of these sums is.

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