
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 $(2x^{2}-x+1)(1-2x)^{6}=a\_{0}+a\_{1}x+a\_{2}x^{2}+…+a\_{8}x^{8}$.
(1) Find $a\_{2}$;
(2) Find $(a\_{2}+a\_{4}+a\_{6}+a\_{8})^{2}-(a\_{1}+a\_{3}+a\_{5}+a\_{7})^{2}$.

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