
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 vectors $\overrightarrow{m}=( \sqrt {3}\sin \dfrac {x}{4},1)$ and $\overrightarrow{n}=(\cos \dfrac {x}{4},\cos ^{2} \dfrac {x}{4})$, and function $f(x)= \overrightarrow{m} \cdot \overrightarrow{n}$.
(I) Find the maximum value of $f(x)$ and the corresponding value of $x$.
(II) In $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. If $f(B)= \dfrac { \sqrt {3}+1}{2}$, $a=2$, and $c=3$, find the value of $\sin A$.

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