
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 that $y+6$ is directly proportional to $x+1$, and when $x=3$, $y=2$.  
$(1)$ Find the functional relationship between $y$ and $x;  
$(2)$ Given the point $\left(m,-2\right)$ lies on the graph of this function, find the value of $m$;  
$(3)$ Determine whether the point $\left(1,-3\right)$ lies on the graph of this function, and provide a reason.

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