
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 expressions: $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}\cdots $. Based on these expressions, what can we infer about the value of $1+\frac{1}{{{2}^{2}}}+\frac{1}{{{3}^{2}}}+\frac{1}{{{4}^{2}}}+\cdot \cdot \cdot +\frac{1}{{{2015}^{2}}} < $ \_\_\_\_\_\_\_\_

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