
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 parabola $C_{1}:\begin{cases}x=8t^{2} \\ y=8t\end{cases} (t$ is the parameter), and the circle $C_{2}$ with the polar equation $\rho=r (r > 0)$, if a line with slope $1$ passes through the focus of the parabola $C_{1}$ and is tangent to the circle $C_{2}$, determine the value of $r$.

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