
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 equations: $$1+ \frac{1}{{2}^{2}} < \frac{3}{2}$$, $$1+ \frac{1}{{2}^{2}}+ \frac{1}{{3}^{2}} < \frac{5}{3}$$, $$1+ \frac{1}{{2}^{2}}+ \frac{1}{{3}^{2}}+ \frac{1}{{4}^{2}} < \frac{7}{4}$$, … Based on these equations, what would be the 2019th equation?

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