
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 line $ax+by+c-1=0$ where $b, c > 0$ passes through the center of the circle $x^{2}+y^{2}-2y-5=0$, find the minimum value of $\frac {4}{b}+\frac {1}{c}$.

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