
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
Let $k=\int_{0}^{\pi}(\sin x-\cos x)dx$, if $(1-kx)^{8}=a_{0}+a_{1}x+a_{2}x^{2}+...+a_{8}x^{8}$, find the value of $a_{1}+a_{2}+a_{3}+...+a_{8}$.

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