
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 propositions:
① The function $f(x) = 4\cos(2x + \frac{\pi}{3})$ has a center of symmetry at $(-\frac{5\pi}{12}, 0)$;
② If $\alpha$ and $\beta$ are angles in the first quadrant, and $\alpha > \beta$, then $\tan\alpha > \tan\beta$;
③ If $|\vec{a} + \vec{b}| = |\vec{a}| - |\vec{b}|$, then there exists a real number $\lambda$, such that $\vec{b} = \lambda \vec{a}$;
④ In $\triangle ABC$, with the sides opposite to angles A, B, C being a, b, c respectively, if $a=40$, $b=20$, and $B=25^\circ$, then $\triangle ABC$ must have two solutions.
⑤ The graph of the function $y = \sin 2x$ is shifted to the left by $\frac{\pi}{4}$ units to obtain the graph of $y = \sin(2x + \frac{\pi}{4})$.

The correct proposition numbers are __________ (fill in all the correct proposition numbers).

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