
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
João wrote down all the powers of 2, 3, and 5 greater than 1 and less than 2017 on a sheet of paper. Then, he performed all possible products of two distinct numbers from that sheet and wrote them on another sheet of paper. What is the number of integers that João recorded on the second sheet?

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