
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 $A=\{x|x^2-3x+2\leq0\}$, $B=\{y|y=x^2-2x+a\}$, and $C=\{x|x^2-ax-4\leq0\}$, let proposition $p$: $A\cap B\neq\emptyset$, and proposition $q$: $A\subseteq C$.  
(1) If proposition $p$ is false, find the range of the real number $a$.  
(2) If the proposition $p\land q$ is true, find the range of the real number $a$.

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