
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 $\frac{{22}}{7}$, $\sqrt{5}$, $0$, $3.1415$, $\sqrt{16}$, $3\pi$, $3.1010010001\ldots$ (where the number of zeros between adjacent ones increases by $1$ each time), calculate the number of irrational numbers.

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