
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 the sequence $\{a_{n}\}$ satisfy $a_{n+1}=a_{n}+2(n+1)$, $n\in \mathbf{N}^{*}$, $a_{1}=2$. Then the sum of the first 40 terms of the sequence $\left\{ (-1)^{n} \cdot a_{n} \right\}$ is __________.

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