
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 $C$: $((x+1)^{2}+(y-2)^{2}=25)$ and point $P(2,1)$
$(I)$ Determine the relationship between point $P$ and the circle;
$(II)$ The chord length cut by the line passing through $P$ on circle $C$ is $8$, find the equation of this line.

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