
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
Given the function $f(x) = |\log_{3}x|$, if $0 < m < n$ and $f(m) = f(n)$, then the range of values for $2m+n$ is \_\_\_\_\_\_.

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