
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 conclusions:  
(1) The inclination angles of lines $l_1$ and $l_2$ are $\alpha_1$ and $\alpha_2$ respectively. If $l_1 \perp l_2$, then $|\alpha_1 - \alpha_2| = 90^\circ$;  
(2) If the inclination angle of the line $(a^2 + 2a)x - y + 1 = 0$ is obtuse, then the range of the real number $a$ is $(-2, 0)$;  
(3) The inclination angle of the line $x\tan \frac{\pi}{7} + y = 0$ is $\frac{6\pi}{7}$;  
(4) Folding a piece of coordinate paper once, making point $(0, 2)$ coincide with point $(4, 0)$, and point $(7, 3)$ coincide with point $(m, n)$, then $m + n = \frac{36}{5}$.  
Among these, the correct conclusion numbers are __________.

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