
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 that $w < 0$ and $|w| < 1$ for the function $f(x) = \sin(wx + \frac{\pi}{4})$.  
(1) If $w = -\frac{1}{2}$, find the minimal positive period, the center of symmetry, and the axis of symmetry for the function $f(x)$.  
(2) If $f(x)$ is monotonically decreasing on the interval $\left(\frac{\pi}{2}, \pi\right)$, find the range of $w$.

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