
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 represented by segments going as follows:
- For $-3 \leq x \leq 0, y = -2 - x$.
- For $0 \leq x \leq 2, y = \sqrt{4 - (x-2)^2} - 2$.
- For $2 \leq x \leq 3, y = 2(x - 2)$.

For certain constants $a$, $b$, and $c$, a new function $g(x)$ is defined by:
\[ g(x) = a f(bx) + c \]
The graph of $y = g(x)$ results from the transformation applied to $y = f(x)$ which stretches it horizontally by a factor of 3, stretches it vertically by a factor of 2, and then shifts the entire graph down by 3 units.

Find the ordered triple $(a, b, c)$.

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