
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 $A=\{x|x^2+2x-8\geq0\}$, $B=\{x| \sqrt{9-3x}\leq \sqrt{2x+19}\}$, $C=\{x|x^2+2ax+2\leq0\}$.  
(1) If the solution set of the inequality $bx^2+10x+c\geq0$ is $A\cap B$, find the values of $b$ and $c$.  
(2) Let the universal set $U=\mathbb{R}$. If $C\subseteq B \cup C_UA$, find the range of the real number $a$.

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