
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
Chinese mathematician Hua Luogeng saw a brain teaser in a magazine that the passenger next to him was reading while on a trip abroad: find the cube root of $59319$. Hua Luogeng blurted out the answer, astonishing everyone. They quickly asked about the calculation's mystery. Do you know how he calculated the result quickly and accurately? Below is Xiaochao's exploration process, please complete it:

$(1)$ Find $\sqrt[3]{59319}$.
① From $10^{3}=1000$ and $100^{3}=1000000$, we can determine that $\sqrt[3]{59319}$ has ____ digits;
② Since the units digit of $59319$ is $9$, we can determine that the units digit of $\sqrt[3]{59319}$ is ____;
③ If we subtract the last three digits $319$ from $59319$ to get $59$, and $3^{3}=27$, $4^{3}=64$, we can determine that the tens digit of $\sqrt[3]{59319}$ is ____, thus obtaining $\sqrt[3]{59319}=\_\_\_\_\_\_$.

$(2)$ Given that $195112$ is also a cube of an integer, using a similar method, we can obtain $\sqrt[3]{195112}=\_\_\_\_\_\_$.

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