
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 ①: If the vector $\overrightarrow{a} \cdot \overrightarrow{b} < 0$, then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is obtuse; Proposition ②: If $\cos \alpha \cdot \cos \beta = 1$, then $\sin (\alpha + \beta) = 0$; Proposition ③: The function $y= \sqrt{x^{2}+9}+ \frac{1}{\sqrt{x^{2}+9}}$ $(x \in \mathbb{R})$ has a minimum value of $2$; Proposition ④: Given $a > 0$, Proposition $p:$ the range of the function $f(x)=\lg (ax^{2}+2a+3)$ is $\mathbb{R}$, Proposition $q:$ the function $g(x)=x+ \frac{a}{x}$ is monotonically increasing in the interval $(1,+\infty)$. If $\neg p \land q$ is true, then the range of the real number $a$ is $(-\infty, \frac{1}{3}]$, the number of true propositions among the above is $\boxed{\text{B: }1}$.

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