
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
Consider the following propositions:
① If $|\vec{a} + \vec{b}| = |\vec{a}| + |\vec{b}|$, then $\vec{a}$ and $\vec{b}$ are collinear and have the same direction;
② The function $f(x) = \cos(\sin x)$ has a smallest positive period of $\pi$;
③ In triangle $\triangle ABC$, if $|\vec{AC}| = 3$, $|\vec{BC}| = 4$, and $|\vec{AB}| = 5$, then $\vec{AB} \cdot \vec{BC} = 16$;
④ The function $f(x) = \tan(2x - \frac{\pi}{3})$ has a center of symmetry at $\left( \frac{5\pi}{12}, 0 \right)$;
Identify the correct propositions by their number.

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