
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 $f(x) = \sin^2\frac{x}{4} - 2\cos^2\frac{x}{4} + \sqrt{3}\sin\frac{x}{4}\cos\frac{x}{4}$, where $x \in \mathbb{R}$.  
(1) Find the interval where the function $y = f(x)$ is decreasing.  
(2) In triangle ABC, the opposite sides of angles A, B, and C are a, b, and c respectively. Given $f(B) = -\frac{1}{2}$ and $b = \sqrt{3}$, find the range of values for the perimeter of triangle ABC.

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