
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 pattern ${1}^{2}=1\phantom{\rule{0ex}{0ex}},{1}^{2}-{2}^{2}=-3,{1}^{2}-{2}^{2}+{3}^{2}=6,{1}^{2}-{2}^{2}+{3}^{2}-{4}^{2}=-10$, find the $n$th equation.

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