
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 for any $x \in \mathbb{R}$, the function $f(x)$ satisfies $f(a+x) = f(a-x)$ (where $a$ is a constant), then the function $f(x)$ must be an even function.
② If for any $x \in \mathbb{R}$, the function $f(x)$ satisfies $f(2+x) = -f(x)$, then the function $f(x)$ is a periodic function.
③ If for any $x_1, x_2 \in \mathbb{R}$, and $x_1 \neq x_2$, it holds that $(x_1 - x_2)[f(x_1) - f(x_2)] < 0$, then the function $f(x)$ is decreasing over $\mathbb{R}$.
④ By translating the graph of the function $y = \log x$ and the graph of the function $y = \log \left( \frac{x + 3}{10} \right)$, the two can be made to coincide.
The numbers of the true propositions are ______.

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