
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
When solving the equation system $\left\{{\begin{array}{l}{ax+5y=15①}\\{4x-by=-2②}\end{array}}\right.$, due to carelessness, person A mistook the value of $a$ in the equation system and obtained the solution $\left\{{\begin{array}{l}{x=-1}\\{y=-1}\end{array}}\right.$. Person B mistook the value of $b$ in the equation system and obtained the solution $\left\{{\begin{array}{l}{x=5}\\{y=2}\end{array}}\right.$. Find the square root of $a+4b$.

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