
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
There are 5 propositions:
① The smallest positive period of the function $y=\sin^4x-\cos^4x$ is $\pi$.
② The set of angles whose terminal sides lie on the y-axis is $\left\{\alpha \mid \alpha = \frac{k\pi}{2}, k \in \mathbb{Z}\right\}$.
③ In the same coordinate system, the graph of the function $y=\sin x$ and the graph of the function $y=x$ have 3 common points.
④ Shifting the graph of the function $y=3\sin\left(2x+ \frac{\pi}{3}\right)$ to the right by $\frac{\pi}{6}$ results in the graph of $y=3\sin 2x$.
⑤ The necessary and sufficient condition for angle $\theta$ to be in the first quadrant is $\sin\theta>0$.
Among these, the numbers of the true propositions are __________ (write down the numbers of all true propositions).

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