
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 $27\;^{\frac{2}{3}} + \lg 5 - 2\log_{2}3 + \lg 2 + \log_{2}9$.
2. Given $f(x) = 3x^2 - 5x + 2$, find $f(-\sqrt{2})$, $f(-a)$, and $f(a+3)$.

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