
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
Let $m$ be an integer such that $m \ge 3.$ For a positive real number $x > 1,$ the generalized Riemann zeta function $\zeta_m(x)$ is defined by
\[\zeta_m(x) = \sum_{n = m}^\infty \frac{1}{n^x}.\]
Compute
\[\sum_{k = 3}^\infty \{\zeta_m(2k - 2)\}.\]
Note: $\{x\}$ denotes the fractional part of $x.$

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