
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
The mathematical giant Euler in history was the first to represent polynomials in terms of $x$ using the notation $f(x)$. For example, $f(x) = x^2 + 3x - 5$, and the value of the polynomial when $x$ equals a certain number is denoted by $f(\text{certain number})$. For example, when $x = -1$, the value of the polynomial $x^2 + 3x - 5$ is denoted as $f(-1) = (-1)^2 + 3 \times (-1) - 5 = -7$. Given $g(x) = -2x^2 - 3x + 1$, find the values of $g(-1)$ and $g(-2)$ respectively.

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