
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 $|A|$ denote the number of elements in a non-empty set $A$, and define $M(a,b) = \begin{cases} a, & \text{if } a \geq b \\ b, & \text{if } a < b \end{cases}$. Given that $A=\{B|B \subseteq \{1,2,3\} \text{ and } B \text{ contains at least one odd number}\}$ and $C=\{x|x^2-4|x|+3=0\}$, determine the possible values of $M(|A|,|C|)$.

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