
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 circle $C$: $x^{2}+y^{2}+Dx-6y+1=0$, its circumference is bisected by the line $x-y+4=0$, and there is exactly one point on circle $C$ that has a distance of $1$ to line $l$: $3x+4y+c=0$. Find the value of $c$.

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