
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 a ray \(O A: y=k x (k>0, x>0)\) and another ray \(O B: y=-k x (x>0)\), a moving point \(P(x, y)\) is inside \(\angle AO x\). Let \(PM \perp OA\) and \(PN \perp OB\) with the feet of the perpendiculars being \(M\) and \(N\) respectively. The area of quadrilateral \(OMPN\) is exactly \(k\).

(1) When \(k\) is a constant, find the explicit function \(y=f(x)\) for the y-coordinate of the moving point \(P\) in terms of its x-coordinate \(x\).

(2) Determine the domain of the function \(y=f(x)\) based on the range of values for \(k\).

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