
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
Proposition $p$: $\forall x > 0, x + \frac{1}{x} > a$; Proposition $q$: $\exists x_0 \in R, x_0^2 - 2ax_0 + 1 \leqslant 0$. If $\neg q$ is a false proposition and $p \wedge q$ is a false proposition, find the range of values for $a$.

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