
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
Let $a$, $b$, $c$ be real numbers. Consider the following propositions:
① If $a > 0$, then the function $f(x) = ax + b$ is monotonic on $\mathbb{R}$.
② If the function $f(x) = ax + b$ is monotonic on $\mathbb{R}$, then $a > 0$.
③ If $b^2 - 4ac < 0$, then $a^3+ab+c \neq 0$.
④ If $a^3+ab+c \neq 0$, then $b^2 - 4ac < 0$.

Identify the true propositions.

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