
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:

\\((1+1)=2×1\\)，

\\((2+1)(2+2)=2^{2}×1×3\\)，

\\((3+1)(3+2)(3+3)=2^{3}×1×3×5\\)，

\\(……\\)

What could be the $n^{th}$ equation according to this pattern?

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