
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 $y-1$ is directly proportional to $x+2$, and when $x=1$, $y=7$.  
$(1)$ Find the functional relationship between $y$ and $x.  
$(2)$ Let the point $\left(a,-2\right)$ lie on the graph of the function obtained in $(1)$, find the value of $a$.

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