
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 system of linear equations in two variables $x$ and $y$:

$\left\{\begin{array}{l}3x-5y=36\\ bx+ay=-8\end{array}\right.$

is equivalent to the system:

$\left\{\begin{array}{l}2x+5y=-26\\ ax-by=-4\end{array}\right.$

$(1)$ Find the common solution to these two systems of equations.  
$(2)$ Find the value of $\left(2a+b\right)^{2023}$.

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