
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}
user