
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 the numbers $0$, $-\frac{11}{7}$, $\frac{π}{2}$, $0.\overline{1}3$, $3.1415$, $2.3\%$, $0.10010001\ldots$ (where the number $1$ increases by $1$ zero between adjacent $1$'s), determine the number of irrational numbers among them.

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