
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) Calculate: $$\frac{\lg \sqrt{27} + \lg 8 - \log_{4}8}{\frac{1}{2}\lg 0.3 + \lg 2}$$;
(2) The function $f(x)$ satisfies $f(x + 1) + f(x - 1) = x^2 - 4x$; find the analytic expression for $f(x)$.

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