
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
Observing the following equations:
$$
\begin{align*}
1^2 &= \frac{1 \times 2}{2} \
1^2 - 2^2 &= -\frac{2 \times 3}{2} \
1^2 - 2^2 + 3^2 &= \frac{3 \times 4}{2} \
1^2 - 2^2 + 3^2 - 4^2 &= -\frac{4 \times 5}{2} \
\end{align*}
$$
Following this pattern, determine the $n^{\text{th}}$ equation.

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