
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) A linear function $f(x)$ satisfies the equation $3f(x+1) - 2f(x-1) = 2x + 17$. Find the expression for $f(x)$.
(2) A function $f(x)$, defined in the interval $(-1, 1)$, satisfies the equation $2f(x) - f(-x) = \log(x+1)$. Find the expression for $f(x)$.
(3) Given that $f(2x+1) = 4x^2 + 8x + 3$, find the expression for $f(x)$.

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