
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: $(2x-1)^{n}=a\_0+a\_1x+a\_2x^{2}+...+a\_n x^{n} (n\in\mathbb{N}^*, n$ is a constant$)$.
(1) Find $|a\_0|+|a\_1|+|a\_2|+...+|a\_n|$;
(2) We know the expansion of the binomial $(1+x)^{n}$ is $(1+x)^{n}=C\_n^{0}+C\_n^{1}x+C\_n^{2}x^{2}+...+C\_n^{n}x^{n}$. If both sides of the equation are differentiated with respect to $x$, we get: $n(1+x)^{n-1}=C\_n^{1}+2C\_n^{2}x+3C\_n^{3}x^{2}...+nC\_n^{n}x^{n-1}$. Let $x=1$, we have $C\_n^{1}+2C\_n^{2}+3C\_n^{3}...+nC\_n^{n}=n\cdot 2^{n-1}$. Use this method to solve the following problems:
$\quad$(a) Find $1a\_1+2a\_2+3a\_3+...+na\_n$;
$\quad$(b) Find $1^{2}a\_1+2^{2}a\_2+3^{2}a\_3+...+n^{2}a\_n$.

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