
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
Solve the following system of equations or inequalities:<br/>$(1)$ Solve the system of equations: $\left\{{\begin{array}{l}{3x+2y=13}\\{2x+3y=-8}\end{array}}\right.$;<br/>$(2)$ Solve the system of inequalities: $\left\{{\begin{array}{l}{\frac{{5y-2}}{3}-1>\frac{{3y-5}}{2}}\\{2(y-3)\leq 0}\end{array}}\right.$.

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