
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
Among the real numbers $\frac{\pi}{2}$, $\frac{22}{7}$, $0.1414$, $\sqrt[3]{9}$, $\sqrt{\frac{1}{2}}$, $-\frac{5}{2}$, $0.1010010001…$, $-\sqrt{\frac{1}{16}}$, $0$, $1- \sqrt{2}$, $\frac{\sqrt{5}}{2}$, $|\sqrt{4}-1|$, which ones are irrational numbers?

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