
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 two sets: $A=\{x \mid -4 \leq x - 6 \leq 0\}$ and $B=\{x \mid 2x - 6 \geq 3 - x\}$.
1. Find the complement of $A \cap B$ in $\mathbb{R}$.
2. If $C=\{x \mid x \leq a\}$ and $A \cap C = A$, find the range of the real number $a$.

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