
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 \( f(x) \) is an odd function defined on \( \mathbb{R} \). For \( x \leqslant 0 \):
\[ 
f(x) = \left| x + \frac{1}{2} \sin \alpha \right| + \left| x + \frac{3}{2} \sin \alpha \right| - 2 \sin \alpha,
\]
where \( \alpha \in (-\pi, \pi) \). If for any real number \( x \), \( f(x) \geqslant f(x+2) \), determine the range of values for \( \alpha \).

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