
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 that point $A(3,1)$ is on the line $mx + ny + 1 = 0$, where $mn > 0$, find the maximum value of $\frac{3}{m} + \frac{1}{n}$.

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