
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 point P(0, 4) is outside the circle C: $x^2+y^2+6x-8y+m=0$.
(1) Find the range of the real number $m$;
(2) If $m=24$, find the minimum value of $x^2+y^2$;
(3) Under the condition of question (2), find the range of $\frac{y-4}{x}$.

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