
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
Among the following propositions, the true ones are numbered \_\_\_\_\_\_\_\_.

1. In $\Delta ABC$, "If $A > 30^{\circ}$" is a sufficient but not necessary condition for "$\sin A > \frac{1}{2}$";
2. Given $\overrightarrow{AB} =(3,4)$, $\overrightarrow{CD} =(-2,-1)$, then the projection of $\overrightarrow{AB}$ on $\overrightarrow{CD}$ is $-2$;
3. Given $p: \exists x \in \mathbb{R}, \cos x = 1$, $q: \forall x \in \mathbb{R}, x^2 - x + 1 > 0$, then "$p \land \neg q$" is a false proposition;
4. The negation of "If $x^2 + x - 6 \geqslant 0$ then $x > 2$";
5. Given the function $f(x) = \sin (\omega x + \frac{\pi}{6}) - 2$ ($\omega > 0$), the maximum value of its derivative is $3$, then the graph of $f(x)$ is symmetric about $x= \frac{\pi}{3}$.

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