
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
Given the arithmetic sequence {a<sub>n</sub>}, a<sub>3</sub>=4, a<sub>2</sub>+a<sub>5</sub>=9, find S<sub>2019</sub>, the sum of the first 2019 terms of the sequence {b<sub>n</sub>}, where b<sub>n</sub>=\frac{1}{a<sub>n</sub><sup>2</sup>-1}.

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