
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 graph of the function $f(x) = \log_{a}(4x-3) + 1$ ($a > 0$ and $a \neq 1$) has a fixed point $A(m,n)$, find the minimum value of $\frac{1}{x+1} + \frac{1}{y}$, where $mx + ny = 3$ for any positive numbers $x$ and $y$.

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