
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
Observing the following inequalities: $(1+\frac{1}{2^2} < \frac{3}{2})$, $(1+\frac{1}{2^2}+\frac{1}{3^2} < \frac{5}{3})$, $(1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2} < \frac{7}{4})$, ..., what is the fifth inequality in this pattern?

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