
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 that the domain of the function $f(x)$ is $\mathbb{R}$, and $2f(x) \cdot 2f'(x) > 2$, $f(0)=8$, solve the inequality $\dfrac{f(x)-1}{e^{\ln 7-x}} > 1$.

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