
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
Given three sets $A = \{0,1,2,4,5,7\}$, $B = \{1,3,6,8,9\}$, and $C = \{3,7,8\}$, find the set $(A \cap B) \cup C$ and the set $(A \cup C) \cap (B \cup C)$.

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