
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 that line $l$ passes through points $P(2,1)$ and $Q(1,-1)$, find the equation of the line. Additionally, find the area of the circle $x^{2}+y^{2}=R^{2}(R > 0)$ for which the chord formed by the intersection with line $m$ (perpendicular to line $l$ and passing through point $P$) has a length of $\frac{6\sqrt{5}}{5}$.

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