
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
Given the sequence $1$, $-2$, $2$, $-3$, $3$, $-3$, $4$, $-4$, $4$, $-4$, $5$, $-5$, $5$, $-5$, $5$, ... alternates in sign, and the absolute value of the terms is $1$ of $1$, $2$ of $2$, $3$ of $3$, ..., $n$ of $n$, find the sum of the first $100$ terms of this sequence.

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