
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
Mathematician Taylor from the UK discovered the following formulas: ${e}^{x}=1+\frac{x}{1!}+\frac{{x}^{2}}{2!}+\frac{{x}^{3}}{3!}+⋯$, $sinx=x-\frac{{x}^{3}}{3!}+\frac{{x}^{5}}{5!}-\frac{{x}^{7}}{7!}+⋯$, $\cos x=1-\frac{{x}^{2}}{2!}+\frac{{x}^{4}}{4!}-\frac{{x}^{6}}{6!}+⋯$, where $n!=1\times 2\times 3\times \cdots \times n$. It can be seen that the more terms on the right side of these formulas are used, the more accurate the values of $e^{x}$, $\sin x$, and $\cos x$ are calculated. Therefore, the approximate value of $\cos 1$ is ______ (accurate to $0.01$); using the above idea, it can be obtained that the function $f(x)={e}^{x}-\frac{1}{x}$ has ______ zero points in the interval $(\frac{2}{3},1)$.

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