
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 binomial $(ax+b)^{n}=a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+…+a_{n}x^{n}(a，b∈R，n∈N^{*})$.

(1) When $a=b=1$, $n=6$, find:
  ① The value of $a_{1}+a_{2}+a_{3}+…+a_{n}$.
  ② The value of $a_{1}+2a_{2}+3a_{3}+…+na_{n}$.

(2) When $a=1$, $b=- \sqrt {3}$, $n=8$, find the value of $(a_{0}+a_{2}+a_{4}+a_{6}+a_{8})^{2}-(a_{1}+a_{3}+a_{5}+a_{7})^{2}$.

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