
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
Let  $f (x)$  be a function mapping real numbers to real numbers. Given that  $f (f (x)) =\frac{1}{3x}$ , and  $f (2) =\frac19$ , find  $ f\left(\frac{1}{6}\right)$ .

*Proposed by Zachary Perry*

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