
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
1. Given $f\left(x + \frac{1}{x}\right) = x^2 + \frac{1}{x^2}$, determine the explicit expression for $f(x)$.
2. Given $f\left(\frac{2}{x}+1\right) = \lg x$, determine the explicit expression for $f(x)$.
3. Given $f(x)$ is a linear function, and satisfies $3f(x+1) - 2f(x-1) = 2x + 17$, determine the explicit expression for $f(x)$.
4. Given a function $f(x)$ defined on the interval $(-1, 1)$ that satisfies $2f(x) - f(-x) = \lg(x+1)$, determine the explicit expression for $f(x)$.

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