
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 linear equations in two variables $x$ and $y$: $\left\{\begin{array}{l}{x+3y=7}\\{x-3y+mx+3=0}\end{array}\right.$.<br/>$(1)$ Write down all positive integer solutions of the equation $x+3y=7$;<br/>$(2)$ If the solution of the system satisfies $2x-3y=2$, find the value of $m$.

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