
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 $xOy$, the graph of the function $y=kx+b\left(k\neq 0\right)$ passes through the points $A\left(0,1\right)$ and $B\left(1,2\right)$, and intersects a line passing through the point $\left(0,4\right)$ and parallel to the x-axis at point $C$. <br/>$(1)$ Find the analytical expression of the function and the coordinates of point $C$; <br/>$(2)$ When $x \lt 3$, for each value of $x$, the value of the function $y=\frac{2}{3}x+n$ is greater than the value of the function $y=kx+b\left(k\neq 0\right)$ and less than $4$, write down the value of $n$ directly.

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