
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 circle $C: (x-3)^2 + (y-4)^2 = 25$, the shortest distance from a point on circle $C$ to line $l: 3x + 4y + m = 0 (m < 0)$ is $1$. If point $N(a, b)$ is located on the part of line $l$ in the first quadrant, find the minimum value of $\frac{1}{a} + \frac{1}{b}$.

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