
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 $f(x)=\begin{cases} x^{\frac{1}{2}}, & x\in[0,+\infty) \\ |\sin x|, & x\in\left(-\frac{\pi}{2},0\right) \end{cases}$, if $f(a)= \frac{1}{2}$, then $a=$ _______.

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