
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
In the real numbers $\frac{27}{5}$, $-\sqrt{4}$, $0$, $\sqrt{8}$, $\frac{π}{2}$, $1.12112111211112\ldots$ (with an extra $1$ between every two $2$'s), there are ______ irrational numbers.

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