
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 $f(x)=3ax^{2}-2(a+b)x+b$, where $0 \leqslant x \leqslant 1$, $a > 0$, and $b$ is any constant.
(I) If $b= \dfrac {1}{2}$, $f(x)=|x- \dfrac {1}{2}|$ has two distinct solutions in $x \in [0,1]$, find the range of the real number $a$.
(II) When $|f(0)| \leqslant 2$ and $|f(1)| \leqslant 2$, find the maximum value of $|f(x)|$.

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