
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. The domain of the function $f(x)=\ln (1+x)-\frac{1}{x}$ is \_\_\_\_\_\_\_\_\_\_\_\_\_
2. The maximum value of the function $f\left( x \right)=\sin^{2}x+\sqrt{3}\cos x-\frac{3}{4}\left( x\in \left[ 0,\frac{\pi }{2} \right] \right)$ is \_\_\_\_\_\_\_\_\_\_
3. The number of incorrect statements among the following four is \_\_\_\_\_\_
   1. If $A=\left\{\left(x,y\right)|x+y=4\right\},B=\left\{\left(x,y\right)|x-2y=1\right\}$, then $A\cap B=\left\{3,1\right\}$;
   2. $\cos 1 < \sin 1 < \tan 1$
   3. The function $y=\sin x$ is monotonically increasing in the first quadrant;

   $④$ The function $f(x)=x^{3}$ has a unique zero point $(0,0)$ in $R$

1. The function $f\left( x \right)$ is an odd function and satisfies $f(x+2)=\frac{1}{f(x)}$, when $0 < x < 2$, $f(x)=-\log_{2}x$, then the value of $({2}^{1+f(\frac{7}{3})})$ is \_\_\_\_\_\_\_

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