
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 graph of $y = f(x)$ is defined as follows:
- For $x$ from -3 to 0, $y = -2 - x$,
- For $x$ from 0 to 2, $y = \sqrt{4 - (x - 2)^2} - 2$,
- For $x$ from 2 to 3, $y = 2(x - 2)$.

The graph of $y = g(x)$ is a transformation of $y = f(x)$. First, reflect $y = f(x)$ across the x-axis, then shift it 3 units to the right. What is $g(x)$ in terms of $f(x)$?

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