
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 function $f(x)=\frac{\sin(\pi+x)-\sqrt{3}\cos{x}\sin{2x}}{2\cos(\pi-x)}-\frac{1}{2}$.

1. Find the smallest positive period and the monotonically decreasing interval of the function $f(x)$.
2. When $x \in (0, \frac{\pi}{2})$, find the maximum value of $f(x)$ and the corresponding value of $x$.

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