
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 a function $f(x)$ defined on the domain $(0, +\infty)$ whose graph passes through the point $(2,4)$, and for all $x \in (0, +\infty)$, $f'(x) > 1$. Determine the solution set of the inequality $f(2^x - 2) < 2^x$.

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