
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:
$$
\begin{align*}
(1+1) &= 2 \times 1 \\
(2+1)(2+2) &= 2^{2} \times 1 \times 3 \\
(3+1)(3+2)(3+3) &= 2^{3} \times 1 \times 3 \times 5
\end{align*}
$$
...
Following this pattern, the nth equation can be written as __________________.

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