
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 the graph of a linear function passes through the points $\left(-3,2\right)$ and $\left(1,-6\right)$.
$(1)$ Determine the expression of the linear function;
$(2)$ If the graph of the linear function intersects the $x$-axis at point $A$ and the $y$-axis at point $B$, with the origin denoted as $O$, find the area of $\triangle OAB$;
$(3)$ If $-5\leqslant x\leqslant 3$, find the maximum value of the function $y$.

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