
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 $f(x) = x^2 + ax + b$ ($a, b \in \mathbb{R}$), and $g(x) = 2x^2 - 4x - 16$,

(1) Find the solution set of the inequality $g(x) < 0$;  
(2) If $|f(x)| \leq |g(x)|$ holds for any $x \in \mathbb{R}$, find $a$ and $b$;  
(3) Under the condition of (2), if $f(x) \geq (m + 2)x - m - 15$ holds for all $x > 2$,  
find the range of the real number $m$.

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