
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 proposition p: ∀x∈R, ax<sup>2</sup>+ax+1＞0, and proposition q: |2a-1|＜3.
(1) If proposition p is true, find the range of values for the real number a.
(2) If p∨q is true, and p∧q 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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