
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
Let $(1-x)^n = a_0 + a_1x + a_2x^2 + \ldots + a_nx^n$, where $n \in \mathbb{N}^*$ and $n \geq 2$.
1. Let $n=11$, find the value of $|a_6| + |a_7| + |a_8| + |a_9| + |a_{10}| + |a_{11}|$;
2. Let $b_k = \frac{k+1}{n-k}a_{k+1}$ (where $k \in \mathbb{N}$, $k \leq n-1$), and $S_m = b_0 + b_1 + b_2 + \ldots + b_m$ (where $m \in \mathbb{N}$, $m \leq n-1$), find the value of $\left| \frac{S_m}{C_{n-1}^m} \right|$.

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