
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 following four propositions:
① For vectors $\overrightarrow{a}$, $\overrightarrow{b}$, $\overrightarrow{c}$, if $\overrightarrow{a} \parallel \overrightarrow{b}$ and $\overrightarrow{b} \parallel \overrightarrow{c}$, then $\overrightarrow{a} \parallel \overrightarrow{c}$;
② If the set of angles A = {$\alpha | \alpha = \frac{k\pi}{2} + \frac{\pi}{4}, k \in \mathbb{N}$}. B = {$\beta | \beta = k\pi \pm \frac{\pi}{4}, k \in \mathbb{Z}$}, then A = B;
③ The graph of the function $y = 2^x$ has exactly 2 common points with the graph of the function $y = x^2$;
④ Shifting the graph of the function $f(-x)$ to the right by 2 units results in the graph of $f(-x+2)$.
The correct propositions are \_\_\_\_\_\_ . (Please list all the correct proposition numbers)

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