
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 $f(x)=\ln x - \frac{x}{a}$ (a > 0), if there exists an $x_0 \in R$ such that for all $x_1 \in [1,2]$, $f(x_1) < f(x_0)$, determine the range of values for the real number $a$.

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