
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 within certain intervals:
\[ 
f(x) = 
\begin{cases} 
-2 - x & \text{for } -3 \leq x \leq 0 \\
\sqrt{4 - (x - 2)^2} - 2 & \text{for } 0 \leq x \leq 2 \\
2(x - 2) & \text{for } 2 \leq x \leq 3 
\end{cases}
\]

For certain constants $a$, $b$, and $c$, a new function $g(x) = af(bx) + c$ is formed, and the transformation results in the graph of $y = g(x)$: stretching the original graph horizontally by factor of 3 and shifting it upwards by 2 units.

Determine the values of $a$, $b$, and $c$ so that the modified graph $y = g(x)$ meets the description.

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