
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
In scientific research, discovering and solving problems is an important driving force for the progress of human civilization. Please observe the following equations first, find the pattern, and answer the questions.  
①$1^{3}=1^{2}$; ②$1^{3}+2^{3}=3^{2}$; ③$1^{3}+2^{3}+3^{3}=6^{2}$; ④$1^{3}+2^{3}+3^{3}+4^{3}=10^{2}$; ⑤$\ldots $  
$(1)$ Equation ⑤ is ______;  
$(2)$ Apply the pattern to find the value of $6^{3}+7^{3}+8^{3}+9^{3}+10^{3}$.

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