
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
It is said that our famous mathematician, Hua Luogeng, saw a puzzle in a magazine that a passenger next to him was reading during a trip abroad. The puzzle was: a number is $59319$, and the cube root of it is sought. Hua Luogeng blurted out: $39$. The passenger next to him was very surprised and asked about the calculation. Hua Luogeng explained the calculation process:<br/>Step 1: Because $10^{3}=1000$, $100^{3}=1000000$, $1000 \lt 59319 \lt 1000000$, so $10＜\sqrt[3]{{59319}}＜100$.<br/>Step 2: Because the unit digit of $59319$ is $9$, the unit digit of the cube of a number with a unit digit of $9$ is $9$, so the unit digit of $\sqrt[3]{{59319}}$ is $9$.<br/>Step 3: If we remove the last three digits $319$ from $59319$, we get the number $59$, and since $3^{3}=27$, $4^{3}=64$, so $30＜\sqrt[3]{{59000}}＜40$,<br/>thus $30＜\sqrt[3]{{59319}}＜40$, which means the tens digit of $\sqrt[3]{{59319}}$ is $3$.<br/>Therefore, $\sqrt[3]{{59319}}=39$.<br/>Please answer the following questions based on the above material:<br/>$(1)$ Using the above method, determine the unit digit of the cube root of $4913$ is ______.<br/>$(2)$ Using the above method, determine the cube root of $50653$ is ______.<br/>$(3)$ Find the value of $\sqrt[3]{{110592}}$, and show the calculation process.

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