
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 puzzle 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 $39$, and the passenger next to him asked about the calculation process.<br/>$(1)$ Below is the process of exploring $\sqrt[3]{{59319}}$, please complete it: ① From $10^{3}=1000$ and $100^{3}=1000000$, it can be determined that $\sqrt[3]{{59319}}$ is a two-digit number; ② Since the unit digit of $59319$ is $9$, it can be determined that the unit digit of $\sqrt[3]{{59319}}$ is $9$; ③ If we subtract the last three digits $319$ from $59319$ to get $59$, and since $3^{3}=27$ and $4^{3}=64$, it can be determined that the tens digit of $\sqrt[3]{{59319}}$ is ______; thus, we find $\sqrt[3]{{59319}}=39$.<br/>$(2)$ Given that $103823$ is also a cube of an integer, please use a similar method to find $\sqrt[3]{{103823}}=\_\_\_\_\_\_$.

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