
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 the derivative of the function $f(x)$, and $f'(x) > 2f(x)$ ($x \in \mathbb{R}$), $f\left(\frac{1}{2}\right) = e$ (where $e$ is the base of the natural logarithm), then the solution set of the inequality $f(\ln x) < x^2$ is \_\_\_\_\_\_.

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