
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:  
$3^2 - 1^2 = 4 \times 2$  
$4^2 - 2^2 = 4 \times 3$  
$5^2 - 3^2 = 4 \times 4$  
…  
If you notice any pattern, please express it using an equation that includes $n$ (where $n \geq 1$ is an integer), and write out the 12th equation.

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