
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 sets $A=\{x|x^2+5x+6\leq0, x\in\mathbb{R}\}$, $B=\{y|y= \sqrt {-x^{2}+2x+15}\}$, $C=\{x|a<x<a+1, x\in\mathbb{R}\}$, find the range of the real number $a$ such that $(A\cup B)\cap C=\emptyset$ holds.

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