
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 $M=\{x|1\leqslant x\leqslant 10, x\in N\}$, for its non-empty subset $A$, each element $k$ in $A$ is multiplied by $\left(-1\right)^{k}$ and then summed up, determine the total sum of these sums for all non-empty subsets of $M$.

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