
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 curve $C$: $\frac{x|x|}{a^{2}} - \frac{y|y|}{b^{2}} = 1$, provide the following conclusions:
1. A line vertical to the $x$-axis intersects the curve $C$ at only one point
2. The line $y = kx + m (k, m \in \mathbb{R})$ intersects the curve $C$ at a maximum of three points
3. The curve $C$ is symmetric with respect to the line $y = -x$
4. For any two points $P_1(x_1, y_1)$ and $P_2(x_2, y_2)$ on the curve $C$, $\frac{y_1 - y_2}{x_1 - x_2} > 0$
Write the sequence number(s) of the correct conclusion(s) ________.

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