
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 $U=\{1,2,3,4,5,6,7,8\}$, and let $A \subseteq U$, $B \subseteq U$, satisfying $A \cap B = \{3\}$, $(\complement_U B) \cap A = \{1,2\}$, and $(\complement_U A) \cap B = \{4,5\}$. Determine the value of $\complement_U (A \cup B)$.

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