
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. For example, if $A=\{1,4,7\}$, the sum can be calculated as $\left(-1\right)^{-1}\times 1+\left(-1\right)^{4}\times 4+\left(-1\right)^{7}\times 7=-4$. Find the total sum of these sums for all non-empty subsets of $M$.

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