
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
Find the sum of the first 100 terms of the sequence $\left\{ \frac{1}{a_na_{n+1}} \right\}$, given that the sequence $\{a_n\}$ is arithmetic, $a_5=5$, and the sum of the first 5 terms of $\{a_n\}$ is $S_5=15$.

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