
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
If  $\zeta$  denote the Riemann Zeta Function, and  $s>1$  then   $$ \sum \limits_{k=1}^{\infty} \frac{1}{1+k^s}\geq \frac{\zeta (s)}{1+\zeta (s)} $$  

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