
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 $f(x)=\sin ( \dfrac{πx}{4}- \dfrac{π}{6})-2{\cos }^{2} \dfrac{πx}{8}+1$.

(1) Find the minimal positive period of $f(x)$.

(2) If the graph of $y=g(x)$ is symmetric to the graph of $y=f(x)$ about the line $x=1$, find the maximum value of $y=g(x)$ when $x\in[0, \dfrac{4}{3}]$.

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