
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 $f(a) = \left(\sqrt{\frac{1-\sin \alpha }{1+\sin \alpha }}+\sqrt{\frac{1+\sin \alpha }{1-\sin \alpha }}\right)\cos^{3} \alpha + 2\sin \left(\frac{\pi }{2}+\alpha \right)\cos \left(\frac{3\pi }{2}-\alpha \right)$ (where $\alpha$ is an angle in the third quadrant)

(I) If $\tan \alpha = 3$, find the value of $f(\alpha)$;

(II) If $f(\alpha) = \frac{14}{5}\cos \alpha$, find the value of $\tan \alpha$.

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