
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 proposition $p$: "There exists $a \gt 0$ such that the function $f\left(x\right)=ax^{2}-4x$ is monotonically decreasing on $\left(-\infty ,2\right]$", and proposition $q$: "There exists $a\in R$ such that for all $x\in R$, $16x^{2}-16\left(a-1\right)x+1\neq 0$". If the proposition "$p\wedge q$" is a true proposition, find the range of real numbers for $a$.

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