
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 negation of the proposition "There exists $x_0 > 0$ such that $x_0^2 + 1 > 3x_0$" is "For all $x \leq 0$, $x^2 + 1 \leq 3x$; 2. If the function $f(x) = e^x$, then for all $x_1, x_2 \in \mathbb{R}$, $f(\frac{x_1 + x_2}{2}) \leq \frac{f(x_1) + f(x_2)}{2}$; 3. The graphs of the functions $y = f(-x + 2)$ and $y = f(x - 2)$ are symmetric about the $y$-axis; 4. The condition "$a = 1$" is a necessary but not sufficient condition for the function $f(x) = \cos^2 ax - \sin^2 ax$ to have a minimum positive period of "$\pi$". Determine the sequence number(s) of the true proposition(s).

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