
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\\times 1\\)

\\(( 2+1 )( 2+2 )={{2}^{2}}\\times 1\\times 3\\)

\\(( 3+1 )( 3+2 )( 3+3 )={{2}^{3}}\\times 1\\times 3\\times 5\\)

\\(\cdots \\)

According to this pattern, the $n^{\text{th}}$ equation can be \_\_\_\_\_\_\_\_．

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