
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 with $x$ and $y$: $\left\{\begin{array}{l}5x+2y=11a+18\\2x-3y=12a-8\end{array}\right.$, where the solutions satisfy $x \gt 0$, $y \gt 0$. Find the range of real number $a$.

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