
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
Two people, A and B, solved the system of equations $\left\{\begin{array}{l}{ax+5y=15①}\\{4x-by=-2②}\end{array}\right.$ together. A misread the value of $a$ in equation ① and obtained the solution of the system as $\left\{\begin{array}{l}{x=-3}\\{y=-1}\end{array}\right.$. B misread the value of $b$ in equation ② and obtained the solution of the system as $\left\{\begin{array}{l}{x=5}\\{y=4}\end{array}\right.$. Calculate the value of $a^{2023}+(-\frac{1}{10}b)^{2023}$.

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