
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 $f(x)=\dfrac{1-\sqrt{2}\sin (2x-\frac{\pi }{4})}{\cos x}$,

(I) Find the domain of $f(x)$;

(II) Let $\alpha$ be an angle in the fourth quadrant with $\tan \alpha =-\dfrac{4}{3}$, find the value of $f(\alpha)$.

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