
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
For a positive integer  $p$ , define the positive integer  $n$  to be  $p$ -safe if  $n$  differs in absolute value by more than  $2$  from all multiples of  $p$ . For example, the set of  $10$ -safe numbers is  $\{3, 4, 5, 6, 7, 13, 14, 15, 16, 17,23, \ldots \}$ . Find the number of positive integers less than or equal to  $10,000$  which are simultaneously  $7$ -safe,  $11$ -safe, and  $13$ -safe.·

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