
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
A sequence ${a_n}$ has a sum of its first $n$ terms as $S_n$, with $a_1=1$ and $a_{n+1}=2S_n+1$. An arithmetic sequence ${b_n}$ satisfies $b_3=3$ and $b_5=9$.

(I) Find the general terms of the sequences ${a_n}$ and ${b_n}$.

(II) If for any $n \in \mathbb{N}^*$, the inequality $\left(S_n+\frac{1}{2}\right)k \geq b_n$ always holds true, find the range of real number $k$ values.

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