
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
There are two propositions as follows:
Proposition p: For all $x \in \mathbb{R}$, the inequality $ax^2 + ax + 1 > 0$ always holds.
Proposition q: The function $f(x) = 4x^2 - ax$ is monotonically increasing on the interval $[1, +\infty)$.
If the proposition "p ∨ q" is true and "¬p" is also true, determine the range of the real number a.

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