
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 propositions A and B:

A: The solution set of the inequality $x^{2}+(a-1)x+a^{2}\leqslant 0$ regarding $x$ is an empty set.

B: The equation $x^{2}+ \sqrt {2}ax-(a-4)=0$ has two distinct real roots.

1. If both propositions A and B are true, find the range of values for the real number $a$.
2. If one and only one of the propositions A and B is false, find the range of values for the real number $a$.

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