
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
The solution range of the real number $x$ for the inequality $x^2+2x < \frac{a}{b} + \frac{16b}{a}$ to always hold true for any $a, b \in (0, +\infty)$ is $(-\infty, -4) \cup (2, +\infty)$.

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