
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 $P(m,n)$ $(m > 0, n > 0)$ is a point on the tangent line to the graph of $f(x) = \frac{1}{3} x^3 - \frac{5}{2} x^2 - x + \frac{185}{6}$ at the point $x=5$, find the minimum value of $\frac{1}{m} + \frac{4}{n}$.

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