
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
A certain function  $f$  has the properties that  $f(3x)=3f(x)$  for all positive real values of  $x$ , and that  $f(x)=1-\mid x-2 \mid$  for  $1\leq x \leq 3$ . Find the smallest  $x$  for which  $f(x)=f(2001)$ .

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