
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 an integer \( x \geq 1 \), let \( p(x) \) be the least prime that does not divide \( x \), and define \( q(x) \) to be the product of all primes less than \( p(x) \). In particular, \( p(1)=2 \). For \( x \) such that \( p(x)=2 \), define \( q(x)=1 \). Consider the sequence \( x_{0}, x_{1}, x_{2}, \ldots \) defined by \( x_{0}=1 \) and

\[ x_{n+1}=\frac{x_{n} p(x_{n})}{q(x_{n})} \]

for \( n \geq 0 \). Find all \( n \) such that \( x_{n}=1995 \).

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