
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
Consider the function \( f(x) = |3\{x\} - 1.5| \) where \( \{x\} \) denotes the fractional part of \( x \). Find the smallest positive integer \( n \) such that the equation \[ nf(xf(x)) = x \] has at least 3000 real solutions.

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