
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 equation of the line $l$: $\cos α⋅(x-2)+ \sin α⋅(y+1)=1 (α∈R)$, determine the correct conclusion(s) from the following:

$①$ The line $l$ always passes through a certain fixed point;

$②$ There exist different real numbers $α_{1}$, $α_{2}$, such that the corresponding lines $l_{1}$, $l_{2}$ are parallel;

$③$ There are at least two points in the coordinate plane that are not on the line $l$;

$④$ The line $l$ can represent all lines in the coordinate plane except $x=2$, $y=-1$;

$⑤$ The line $l$ can represent all lines in the coordinate plane.

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