
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 expressions: $1^{2}-1=1\times 0$; $2^{2}-2=2\times 1$; $3^{2}-3=3\times 2$; $4^{2}-4=4\times 3$; $5^{2}-5=5\times 4$; $\ldots$ <br/> According to this pattern, the $n$th (where $n$ is a positive integer) equation is ______.

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