
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 proposition $p$ be: the equation $4x^2 + 4(a-2)x + 1 = 0$ has no real roots; proposition $q$ be: the domain of function $y = \ln(x^2 + ax + 1)$ is $\mathbb{R}$. Determine the range of the real number $a$ if proposition $p$ or proposition $q$ is true.

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