
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
Determine the sum of the following series:
$$
1 \cdot 2-2 \cdot 3+3 \cdot 4-4 \cdot 5+\ldots \pm n(n+1)
$$

(Two cases should be considered, depending on whether \( n \) is an even or odd number.)

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