
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 \( R \) be the reals and \( R^+ \) the positive reals. \( f: R \to R^+ \) is differentiable and \( f'(x) > f(x) \) for all \( x \). For what \( k \) must \( f(x) \) exceed \( e^{kx} \) for all sufficiently large \( k \)?

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