
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
Find all primes  $p \geq 3$  with the following property: for any prime  $q<p$ , the number
\[
p - \Big\lfloor \frac{p}{q} \Big\rfloor q
\]
is squarefree (i.e. is not divisible by the square of a prime).

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