
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 $n \in \mathbb{N}^*$, and $C_{ n }^{ 1 }+2 C_{ n }^{ 2 }+3 C_{ n }^{ 3 }+…+n C_{ n }^{ n }=192$, and $(3-2x)^{n}=a_{0}+a_{1}x+a_{2}x^{2}+…+a_{n}x^{n}$. Find:
  1. The sum of the binomial coefficients in the expansion.
  2. The value of $a_{0}+a_{2}+a_{4}+a_{6}$.
  3. The value of $|a_{0}|+|a_{1}|+…+|a_{n}|$.

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