
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
Given the function $f(x)=\log _{b} \frac {x}{a}(b > 0,b\neq 1)$, whose graph passes through points $A( \frac {1}{4},4)$, $B(1,5)$. Let $a_{n}=f(4^{n})+ \log _{b}a^{2}$, and $S_{n}$ be the sum of the first $n$ terms of the sequence ${a_{n}}$.
(I) Solve the inequality $a_{n}S_{n}\leqslant 0$ with respect to $n$;
(II) Let $b_{n}=2a_{n}S_{n}+2n^{2}(n∈N^{\*)})$, find the minimum value of $b_{n}$.

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