
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 \( f(x) \) defined on the set of real numbers \( \mathbf{R} \) that satisfies \( f^{\prime}(x) - 2 f(x) - 4 > 0 \) and \( f(0) = -1 \), determine the solution to the inequality \( f(x) > e^{2x} - 2 \).

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