
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 $P={x|1≦x≦6,x∈N}$, for its non-empty subset $A$, multiply each element $k$ in $A$ by $(-1)^k$ and then sum them up. (For example, if $A={1,3,6}$, the sum would be $(-1)⋅1+(-1)^3⋅3+(-1)^6⋅6=2$.) The total sum of these sums for all non-empty subsets of $M$ is \_\_\_\_\_\_.

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