
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 that $((x^{2}+1)(2x-1)^{8}=a\_{0}+a\_{1}(x+1)+a\_{2}(x+1)^{2}+…+a\_{10}·(x+1)^{10})$.

(1) Find the value of $a\_{0}+a\_{1}+a\_{2}+…+a\_{10}$;

(2) Find the value of $a\_{0}+a\_{2}+a\_{4}+a\_{6}+a\_{8}+a\_{10}$ and $a\_{1}+a\_{3}+a\_{5}+a\_{7}+a\_{9}$.

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