
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
If the solutions of the system of linear equations in two variables $x$ and $y$, $\left\{\begin{array}{l}3x-y=2a-5\\ x+2y=3a+3\end{array}\right.$, are both positive numbers.<br/>$(1)$ Find the range of values for $a$;<br/>$(2)$ If the solutions of this system form an isosceles triangle with one side being a leg and the other side being the base, and the perimeter of this isosceles triangle is $12$, find the value of $a$.

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