
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
For integers $a$ and $b$, there exists a unique pair of integers $q$ and $r$ such that $a = bq + r$, where $0 \leq r < |b|$. Specifically, when $r = 0$, it is said that $b$ divides $a$, denoted as $b|a$. Given $A = \{1, 2, 3, \ldots, 23\}$:

(Ⅰ) There exists $q \in A$ such that $2011 = 91q + r$ ($0 \leq r < 91$). Try to find the values of $q$ and $r$.

(Ⅱ) If $B \subseteq A$, $\text{card}(B) = 12$ (where $\text{card}(B)$ denotes the number of elements in set $B$), and there exist $a, b \in B$, $b < a$, $b|a$, then $B$ is called a "harmonic set". Please write out a "harmonic set" $B$ that includes the element $7$, a non-"harmonic set" $C$ that includes the element $8$, and find the largest $m \in A$ such that any subset of $A$ containing $m$ with 12 elements is a "harmonic set", and explain the reason.

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