
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 functions $f(x) = x^2 - 2x$ and $g(x) = ax + 2$ (where $a > 0$), for any $x_1 \in \mathbb{R}$, determine the range of values for the real number $a$ such that there exists an $x_2 \in [-2, +\infty)$ such that $f(x_1) > g(x_2)$.

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