
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
A sequence of numbers arranged according to a certain rule is $\frac{1}{2}$, $-\frac{1}{5}$, $\frac{1}{10}$, $-\frac{1}{17}$, $\frac{1}{26}$, $-\frac{1}{37}$, $\ldots$. Continuing this pattern, the $8$th number in this sequence is ____, and the $n$th number is ____ ($n$ is a positive integer).

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