
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 $S_n = \{A | A = (a_1, a_2, \ldots, a_n), a_i = 0 \text{ or } 1, i = 0, 1, 2, \ldots, n\}$. For $U, V \in S_n$, $d(U, V)$ denotes the number of elements in $U$ and $V$ that are different.  
(1) Let $U = \{1, 1, 1, 1, 1, 1\}$. There exist $m$ elements $V \in S_6$ such that $d(U, V) = 2$. Then, $m = \_\_\_\_\_\_$.  
(2) If a certain $U \in S_n$ is given, for any $V \in S_n$, the sum of all $d(U, V)$ is $\_\_\_\_\_\_$.

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