
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 sequence of equations: $a_{1}=1-\frac{1}{3}$, $a_{2}=\frac{1}{2}-\frac{1}{4}$, $a_{3}=\frac{1}{3}-\frac{1}{5}$, $a_{4}=\frac{1}{4}-\frac{1}{6}$, $\ldots$. Try to guess the $n$th equation $(n$ is a positive integer$): a_{n}=$____.

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