
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:  
$15^2 = 1 \times (1 + 1) \times 100 + 5^2 = 225$,  
$25^2 = 2 \times (2 + 1) \times 100 + 5^2 = 625$,  
$35^2 = 3 \times (3 + 1) \times 100 + 5^2 = 1225$,  
...  
According to this pattern, the $n$-th equation (where $n$ is a positive integer) is .

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