
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 line $l: (a-1)x + y - a - 5 = 0$ (where $a$ is a parameter and $a \in \mathbb{R}$),<br/>$(1)$ If the line $l$ always passes through a fixed point $A$ regardless of the value of $x$, find the coordinates of the fixed point $A$;<br/>$(2)$ If the line $l$ does not pass through the second quadrant, find the range of real numbers for $a$.

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