
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
A student, while reviewing the content on functions, came to the following conclusions:
① The function $f(x) = x + \frac{1}{x}$ has a maximum value of -2 on $(-\infty, 0)$;
② The function $f(x) = \frac{1}{\ln(x+2)}$ is a decreasing function on $(-2, +\infty)$;
③ There exists $a \in \mathbb{R}$, such that the function $f(x) = \frac{x}{(2x+1)(x-a)}$ is an odd function;
④ Logarithmic functions have the property "For any real numbers $x, y$, it satisfies $f(xy) = f(x) + f(y)$."
Among these conclusions, the correct ones are __________ (Fill in the serial numbers of the conclusions you think are correct).

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