
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
Divide the elements of the set $M=\{1,2,\ldots,12\}$ into three disjoint subsets: $M=A\cup B\cup C$, where $A=\{a_1,a_2,a_3,a_4\}$, $B=\{b_1,b_2,b_3,b_4\}$, $C=\{c_1,c_2,c_3,c_4\}$, $c_1<c_2<c_3<c_4$, and $a_k+b_k=c_k$ for $k=1,2,3,4$. Then, the set $C$ is: \_\_\_\_\_\_\_\_\_.

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