
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
In the sequence $\{a_{n}\}$, $a_{1}=2$, $a_{3}=26$. If the sequence $\{\log _{3}(a_{n}+1)\}$ forms an arithmetic sequence, then $S_{n}=\frac{1}{a_2-a_1}+\frac{1}{a_3-a_2}+\cdots+\frac{1}{a_{n+1}-a_n}=\_\_\_\_\_\_$.

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