
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 function $\varphi(x) = f(x) + g(x)$, where $f(x)$ is directly proportional to $x$ and $g(x)$ is inversely proportional to $x$, and it is known that $\varphi\left(\frac{1}{3}\right) = 16$ and $\varphi(1) = 8$, find the expression for $\varphi(x)$.

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