
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
Given the following sequence of expressions: 
$$1^3=(1\times1)^2,$$
$$1^3+2^3+3^3=(2\times3)^2,$$
$$1^3+2^3+3^3+4^3+5^3=(3\times5)^2,$$
$$1^3+2^3+3^3+4^3+5^3+6^3+7^3=(4\times7)^2,$$
$$\ldots$$
By induction, the $n$-th expression is __________.

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