
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
Find the value of $-1 + 2 + 3 + 4 + 5 - 6 - 7 - 8 - 9 - 10 - 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 - 20 - 21 - 22 - 23 - 24 - 25 - 26 - 27 + \dots + 10000$, where the sequence of alternating signs changes after each successive triangular number.
1, 3, 6, 10, 15... defines the changing points.

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