
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
Among the following six propositions, the correct ones are:  
① Any straight line in the coordinate plane has an angle of inclination and a slope;  
② The range of values for the angle of inclination of a straight line is $[0°, 180°]$;  
③ If the slope of a straight line is $\tan\alpha$, then the angle of inclination of this line is $\alpha$;  
④ If the slopes of two lines do not exist, then the two lines are parallel;  
⑤ If one of two lines has a non-existent slope and the other has a slope, then the two lines intersect;  
⑥ The equation of the line passing through any two different points $P_1(x_1, y_1)$, $P_2(x_2, y_2)$ is $(x_2-x_1)(y-y_1)=(y_2-y_1)(x-x_1)$.

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