
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
Let $g(x) = \sin{x} - \cos{x} + 4\tan{x}$, using radian measure for $x$. Find the smallest positive value $s$ such that $g(x) = 0$ within the region $\frac{\pi}{2} < x < \frac{3\pi}{2}$, and determine $\lfloor s \rfloor$.

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