
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
Let $n \in \mathbb{N}^+$, and consider the function $f(n) = (-1)^{n-1} \cdot n^2$. If $a_n = f(n) + f(n+1)$, then the sum of the first 100 terms of the sequence $\{a_n\}$, $a_1 + a_2 + a_3 + \ldots + a_{100} = \ $.

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