
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 shown as follows, defined by pieces:

1. From $x = -3$ to $x = 0$: \( f(x) = -2 - x \)
2. From $x = 0$ to $x = 2$: \( f(x) = \sqrt{4 - (x - 2)^2} - 2 \)
3. From $x = 2$ to $x = 3$: \( f(x) = 2(x - 2) \)

For certain constants $a$, $b$, and $c$,
\[ g(x) = af(bx) + c. \]
The modified graph of $y = g(x)$ undergoes a horizontal stretch by a factor of 3, then a downward shift by 3 units. Determine the ordered triple $(a,b,c)$ that represents these transformations.

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