
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
\[
\sum_{k = 3}^{10} \{\zeta(2k)\}.
\]
(Note: For a real number $x,$ $\{x\}$ denotes the fractional part of $x.$)

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