
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 the set $M$, define the function $f_M(x) = \begin{cases} -1, & x \in M \\ 1, & x \notin M \end{cases}$. For two sets $M$ and $N$, define the set $M \triangle N = \{x | f_M(x) \cdot f_N(x) = -1\}$. Given $A = \{2, 4, 6, 8, 10\}$ and $B = \{1, 2, 4, 8, 16\}$.

(1) List the elements of the set $A \triangle B = \_\_\_\_\_$;  
(2) Let $\text{Card}(M)$ represent the number of elements in a finite set $M$. When $\text{Card}(X \triangle A) + \text{Card}(X \triangle B)$ takes the minimum value, the number of possible sets $X$ is $\_\_\_\_\_$.

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