
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
Let \( f(x) \) be an odd function defined on \(\mathbf{R}\) and satisfying \( f(x+2) = -f(x) \). Additionally, for \(0 \leqslant x \leqslant 1\), \(f(x) = \frac{1}{2} x\). Determine the set \(\left\{ x \, \left| \, f(x) = -\frac{1}{2} \right. \right\}\).

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