
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 following two propositions:

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 strictly increasing on the interval $[1,+\infty)$.

If the disjunction "$P \vee Q$" is true and "$\neg P$" is also true, find the range of values for the real number $a$.

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