
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 the system of equations in terms of $x$ and $y$: $\left\{\begin{array}{l}{5x+y=3}\\{ax+5y=4}\end{array}\right.$ and $\left\{\begin{array}{l}{x-2y=5}\\{5x+by=1}\end{array}\right.$ have the same solution, find the value of $\frac{1}{2}a-b$.

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