
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 the universal set U be $\{x \mid x \text{ is a positive integer less than 10}\}$, B be $\{1,2,3,4\}$, and C be $\{3,4,5,6\}$. Determine the following:
(1) Represent the universal set U using the rooster method.
(2) If $D = B \cap C$, list all the subsets of set D.
(3) Find the complement of $B \cap C$ with respect to U.

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