
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 $f(x) = 3 \sin(2x + \varphi)$, where $\varphi \in (-\pi, 0)$, and the axis of symmetry of the graph of $y = f(x)$ is the line $x = \frac{\pi}{8}$.

1. Find the value of $\varphi$.
2. Find the intervals where $y = f(x)$ is decreasing.
3. Find the range of $y = f(x)$ when $x \in [0, \frac{\pi}{2}]$.

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