
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 planar vectors $\overrightarrow{a} = (4\sin(\pi - \alpha), \frac{3}{2})$ and $\overrightarrow{b} = (\cos{\frac{\pi}{3}}, \cos{\alpha})$ with $\overrightarrow{a} \perp \overrightarrow{b}$,

(I) Find the value of $\tan{\alpha}$;
(II) Find the value of $\frac{1}{1 + \sin{\alpha}\cos{\alpha}}$.

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