
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 about $x$ and $y$: $\left\{\begin{array}{l}{2x+y=5a}\\{x-3y=-a+7}\end{array}\right.$.<br/>$(1)$ Find the solution to this system of equations; (express using algebraic expressions containing the letter $a$)<br/>$(2)$ If the solution to this system of equations satisfies $x$ being non-negative and $y$ being negative, find the range of values for the letter $a$.

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