
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 patterns:①$1\times 3-2^{2}=-1$；②$2\times 4-3^{2}=-1$；③$3\times 5-4^{2}=-1\ldots $. According to the above pattern, express the $n$th ($n$ is a positive integer) expression with a formula containing letters as ______.

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