
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
Let \(k, l, m\) be real numbers, with \(m \neq 0\). In a Cartesian coordinate system, the function \(y=f(x)=k + \frac{m}{x-l}\) has a graph denoted as curve \(C_{1}\). Another function \(y=g(x)\) has a graph denoted as curve \(C_{2}\), which is symmetric to \(C_{1}\) with respect to the line \(y=x\). Given that the points \((1,4)\), \((2,3)\), and \((2,4)\) lie on either \(C_{1}\) or \(C_{2}\), find the value of \(f(k+l+m)\).

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