
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 $p$: The domain of the function $f(x)=\lg (ax^{2}-2x+1)$ is $\mathbb{R}$; proposition $q$: When $x\in\left[ \frac{1}{2},\;2\right]$, $x+ \frac{1}{x} > a$ always holds. If the proposition "$p\land q$" is true, then the range of the real number $a$ is \_\_\_\_\_\_.

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