
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
(1) If the proposition "There exists $x \in \mathbb{R}$, such that $2x^2-3ax+9 < 0$ is true" is a false proposition, then the range of values for the real number $a$ is.

(2) Given the function $f(x)=\begin{cases}a^{x} & (x < 0), \\ (a-3)x+4a & (x\geqslant 0)\end{cases}$ satisfies for any $x_{1} \neq x_{2}$, $\dfrac{f(x_{1})-f(x_{2})}{x_{1}-x_{2}} < 0$ holds, then the range of values for $a$ is.

(3) Given the proposition $p$: "For every $x \in \mathbb{R}$, there exists $m \in \mathbb{R}$, such that $4^{x}-2^{x+1}+m=0$", and the negation of proposition $p$ is a false proposition, then the range of values for the real number $m$ is.

(4) $\int_{0}^{\pi} (x+\cos x)dx=$

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