
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
The graph of the function \( f(x)=\sin \left(\frac{\pi}{4} x-\frac{\pi}{6}\right)-2 \cos ^{2} \frac{\pi}{8} x+1 \) is symmetrical with the graph of the function \( y=g(x) \) about the line \( x=1 \). When \( x \in\left[0, \frac{4}{3}\right] \), the maximum value of \( g(x) \) is \(\qquad\) .

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