
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
In the Cartesian coordinate system, the graph of a direct proportion function passes through the point $\left(1,2\right)$. By shifting this direct proportion function $5$ units upwards, we obtain the line $l:y=kx+b\left(k\neq 0\right)$. Line $l$ intersects the $x$-axis at point $A$.  
$(1)$ Find the analytical expression of line $l$.  
$(2)$ Find the coordinates of point $A$.

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