
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 $a\in \mathbb{R}$, and consider the proposition $p$: For all $x\in [1,2]$, it satisfies $(a-1)x-1 > 0$. Proposition $q$: For all $x\in \mathbb{R}$, ${x}^{2}+ax+1 > 0$. If the statement $\neg p \land q$ is false, and $\neg p \vee q$ is true, find the range of values for $a$.

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