
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 sets $A=\{x | x^2 - ax \leq x - a\}$, $B=\{x | 1 \leq \log_2(x+1) \leq 2\}$, $C=\{x | x^2 + bx + c > 0\}$,  
(1) If $A \cap B = A$, determine the range of values for $a$.  
(2) If $B \cap C = \varnothing$ and $B \cup C = \mathbb{R}$, determine the values of $b$ and $c$.

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