
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
Compute the sum:
\[\sum_{k=1}^\infty \{\zeta(2k)\}\]
where $\zeta(x)$ is the Riemann zeta function defined for $x > 1$ by 
\[\zeta(x) = \sum_{n=1}^\infty \frac{1}{n^x}\]
and $\{x\}$ denotes the fractional part of $x$.

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