
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 $U = \mathbb{R}$, $A = \{x \mid x \geq 3\}$, $B = \{x \mid x^2 - 8x + 7 \leq 0\}$, $C = \{x \mid x \geq a - 1\}$  
(1) Find $A \cap B$ and $A \cup B$.  
(2) If $C \cup A = A$, find the range of the real number $a$.

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