
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
Read the following information: Given $x-y=2$, and $x \gt 1$, $y \lt 0$, determine the range of values for $x+y$. The solution is as follows: Solution: Since $x-y=2$, and $x \gt 1$, therefore $y+2 \gt 1$, also since $y \lt 0$, therefore $-1 \lt y \lt 0 \ldots$ (1) Similarly, we get $1 \lt x \lt 2 \ldots$ (2). Adding (1) and (2) gives $-1+1 \lt x+y \lt 0+2$, therefore the range of values for $x+y$ is $0 \lt x+y \lt 2$. Using the above method, solve the following problem: For the system of equations regarding $x$ and $y$: $\left\{\begin{array}{l}{3x-y=2a-5}\\{x+2y=3a+3}\end{array}\right.$, all solutions are positive numbers. (1) Find the range of values for $a$; (2) Given $a-b=4$, and $b \lt 2$, find the range of values for $a+b$.

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