
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 $y$ is directly proportional to $3x-2$, and when $x=2$, $y=8$.  
$(1)$ Find the functional relationship between $y$ and $x$;  
$(2)$ Find the value of the function when $x=-2$;  
$(3)$ If the graph of the function intersects the $x$-axis at point $A$ and the $y$-axis at point $B$, find the area of $\triangle AOB$.

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