
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]


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Given that the derivative of the function $f(x)$ is $f'(x)$, and for all $x \in \mathbb{R}$, the inequality $2f'(x) > f(x)$ holds, find the solution set of the inequality $$e^{ \frac {x-1}{2}}f(x) < f(2x-1).$$

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