
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 four propositions:
1. For the integer coefficient equation $ax^2+bx+c=0$ ($a \neq 0$), if $\Delta$ is a perfect square, then the equation must have rational roots.
2. For the integer coefficient equation $ax^2+bx+c=0$ ($a \neq 0$), if the equation has rational roots, then $\Delta$ is a perfect square.
3. For the irrational coefficient equation $ax^2+bx+c=0$ ($a \neq 0$), the roots can only be irrational numbers.
4. If $a$, $b$, and $c$ are all odd numbers, then the equation $ax^2+bx+c=0$ does not have rational roots.

Among these, the true propositions are.

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