
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
For a positive real number \( x>1 \), the Riemann zeta function \(\zeta(x)\) is defined by
\[ \zeta(x) = \sum_{n = 1}^\infty \frac{1}{n^x}. \]
Compute
\[ \sum_{k = 2}^\infty \{\zeta(2k)\}. \]
(Note: For a real number \( x \), \(\{x\}\) denotes the fractional part of \(x\).)

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