
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:  
$1^2 = 1$  
$1^2 - 2^2 = -3$  
$1^2 - 2^2 + 3^2 = 6$  
$1^2 - 2^2 + 3^2 - 4^2 = -10$  
...  
From the above equations, infer a general conclusion. For $n \in \mathbb{N}^*$, $1^2 - 2^2 + 3^2 - 4^2 + \ldots + (-1)^{n+1}n^2 =$  

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