
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
Observe the following equations:

\\(1- \frac{1}{2}= \frac{1}{2} \\)

\\(1- \frac{1}{2}+ \frac{1}{3}- \frac{1}{4}= \frac{1}{3}+ \frac{1}{4} \\)

\\(1- \frac{1}{2}+ \frac{1}{3}- \frac{1}{4}+ \frac{1}{5}- \frac{1}{6}= \frac{1}{4}+ \frac{1}{5}+ \frac{1}{6} \\)

\\(..........\\)

Based on this pattern, the $n^{th}$ equation can be \_\_\_\_\_\_\_\_\_\_\_.

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