
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
Find the explicit expressions for the following functions:
(1) Given $f(x) = x^{2} + 2x$, find $f(2x+1)$;
(2) Given $f(\sqrt{x} - 1) = x + 2\sqrt{x}$, find $f(x)$;
(3) Given $f(x) - 2f(\frac{1}{x}) = 3x + 2$, find $f(x)$.

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