
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
A new operation is defined for $x$ and $y$ as follows: $F\left(x,y\right)=ax+by$. For example, when $x=-1$ and $y=2$, $F\left(-1,2\right)=a\cdot \left(-1\right)+b\cdot 2=-a+2b$.
$(1)$ If $F\left(-1,3\right)=2$ and $F\left(1,-2\right)=8$, find the values of $a$ and $b$.
$(2)$ If $b$ is a non-negative number and $F\left(2,1\right)=5$, find the range of values for $a$.

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