
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
Let A and B be two sets where A=\{x\mid a\leq x \leq a+4\} and B=\{x\mid x^2-x-6\leq0\}.
1. If a=0, find the intersection A∩B and the union A∪(complement of B in ℝ), 
2. If A∪B=B, find the range for the real number a.

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