
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 The negation of the proposition "For all $x \in \mathbb{R}, \cos x > 0$" is "There exists $x \in \mathbb{R}$ such that $\cos x \leq 0$";  
② If $0 < a < 1$, then the function $f(x) = x^2 + a^x - 3$ has only one zero;  
③ The function $y = \sin(2x - \frac{\pi}{3})$ has a monotonic increasing interval of $\left[- \frac{\pi}{12}, \frac{5\pi}{12}\right]$;  
④ For any real number $x$, if $f(-x) = f(x)$ and $f′(x) > 0$ when $x > 0$, then $f′(x) < 0$ when $x < 0$.  
The numbers of the true propositions are __________ (Fill in the numbers of all true propositions).

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