
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 positive 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 $A = \{1, 2, 3, 4, 5, \ldots, 23\}$, if $M \subseteq A$, and there exist $a, b \in M$, with $b < a$, and $b|a$, then $M$ is called a "harmonic set" of set $A$.  
(1) There exists $q \in A$, such that $2011 = 91q + r$ ($0 \leq r < 91$), try to find the values of $q$ and $r$;  
(2) Given set $B = \{5, 7, 8, 9, 11, 12, t\}$ satisfies $B \subseteq A$, but $B$ is not a "harmonic set", try to write down all possible values of $t$;  
(3) Given set $C$ is a subset of set $A$ with 12 elements, and $m \in A$, when $m \in C$, no matter what the other elements of $C$ are, $C$ is always a "harmonic set" of set $A$, try to find the maximum value of $m$ that satisfies the condition, and briefly explain the reason.

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