
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 the universal set $U = \mathbb{R}$, let $A = \{x \mid 3 \leq x < 7\}$ and $B = \{x \mid 2 < x < 10\}$. Find the complement of $A \cup B$ in $U$, denoted $\complement_U (A \cup B)$, and the intersection of the complement of $A$ in $U$ with $B$, denoted $(\complement_U A) \cap B$.

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