
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 a linear function $y=(3m-2)x+(1-n)$.  
$(1)$ Find the values of $m$ and $n$ for which the graph of the function passes through the origin.  
$(2)$ Find the values of $m$ and $n$ for which $y$ increases as $x$ increases.  
$(3)$ If the graph does not pass through the third quadrant, find the range of values for $m$ and $n$.

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