
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 system of linear equations in two variables $x$ and $y$ $\left\{\begin{array}{l}{2x+5y=-26}\\{ax-by=-4}\end{array}\right.$ and $\left\{\begin{array}{l}{3x-5y=36}\\{bx+ay=-8}\end{array}\right.$ have the same solution, find:<br/>$(1)$ The solution to these two systems of equations;<br/>$(2)$ The value of the algebraic expression $\left(2a+b\right)^{2020}$.

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