
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 function $f(x)$ is considered an "ideal function" if it satisfies the following conditions simultaneously:

1. For any $x$ in its domain, $f(x) + f(-x) = 0$.
2. For any $x_1, x_2$ in its domain, when $x_1 \neq x_2$, it always holds that $\frac{f(x_1) - f(x_2)}{x_1 - x_2} < 0$.

Among the following three functions: (1) $f(x) = \frac{1}{x}$, (2) $f(x) = x^2$, (3) $f(x) = \begin{cases} -x^2, & x \geq 0 \\ x^2, & x < 0 \end{cases}$, the one(s) that can be called "ideal function(s)" is/are \_\_\_\_\_\_. (Fill in the blank with the corresponding number(s).)

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