
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 that $f(\alpha) = \left(\sqrt{\frac{1 - \sin{\alpha}}{1 + \sin{\alpha}}} + \sqrt{\frac{1 + \sin{\alpha}}{1 - \sin{\alpha}}}\right)\cos^3{\alpha} + 2\sin{\left(\frac{\pi}{2} + \alpha\right)}\cos{\left(\frac{3\pi}{2} + \alpha\right)}$ (where $\alpha$ is an angle in the third quadrant),
(I) find the value of $f(\alpha)$ when $\tan{\alpha} = 2$;
(II) find the value of $\tan{\alpha}$ when $f(\alpha) = \frac{2}{5}\cos{\alpha}$.

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