
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
Say a positive integer  $n$  is *radioactive* if one of its prime factors is strictly greater than  $\sqrt{n}$ . For example,  $2012 = 2^2 \cdot 503$ ,  $2013 = 3 \cdot 11 \cdot 61$  and  $2014 = 2 \cdot 19 \cdot 53$  are all radioactive, but  $2015 = 5 \cdot 13 \cdot 31$  is not. How many radioactive numbers have all prime factors less than  $30$ ?

*Proposed by Evan Chen*

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