
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
What is the smallest integer value of \\(m\\) that makes the solutions of the system of equations in \\(x\\) and \\(y\\) \\(\begin{cases} & x+y=2m+7, \\\\ & x-2y=4m-3 \\end{cases}\\) positive integers?

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