
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
For a function, when the independent variable $x$ takes the value $a$, the function value $y$ is also equal to $a$. In this case, the point $(a,a)$ is called a point of the function with the same value. It is known that the quadratic function is $y=x^{2}+3x+m$.  
$(1)$ If the point $(2,2)$ is a point of the function with the same value, then the value of $m$ is ______.  
$(2)$ If this function has two distinct points of the same value $(a,a)$, $(b,b)$, and $a \lt 1 \lt b$, then the range of values for $m$ is ______.

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