
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 parametric equation of parabola C: $$\begin{cases} x=8t^{2} \\ y=8t \end{cases}$$ (where $t$ is the parameter), if a line with a slope of 1 passes through the focus of the parabola C and is tangent to the circle $(x-4)^{2}+y^{2}=r^{2}$ (where $r>0$), then find the value of $r$.

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