
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
Observe the following equations: $2^3-1^3=3\times2\times1+1$, $3^3-2^3=3\times3\times2+1$, $4^3-3^3=3\times4\times3+1$, $5^3-4^3=3\times5\times4+1$, ..., according to this pattern, the $n$th ($n\in\mathbb{N}^*$) equation can be written as "(n+1)$^3$-n$^3$=______".

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