
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 $f(x) = ax^2 + bx - 2b$,
(1) Solve the inequality $f(x) < 0$ for $x$ when $a = b > 0$;
(2) When $a=1$, if the inequality $f(x) \geq 1$ holds for all $x \in (-\infty, 2)$, find the range of the real number $b$;
(3) If $|f(-1)| \leq 1$ and $|f(1)| \leq 3$, find the range of $|a| + |b+2|$.

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