
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 three parts: 
1. A line segment from \( x = -3 \) to \( x = 0 \) with \( f(x) = -2 - x \),
2. A semicircle from \( x = 0 \) to \( x = 2 \) with \( f(x) = \sqrt{4 - (x-2)^2} - 2 \),
3. A line segment from \( x = 2 \) to \( x = 3 \) with \( f(x) = 2(x-2) \).

For particular constants \( a, b, \) and \( c \), consider a new function:
\[ g(x) = a f(bx + 1) + c. \]
The transformed graph of \( y = g(x) \) involves stretching it horizontally by a factor of 3, moving it horizontally to the left by 1 unit, and shifting it down by 3 units. Determine the values of \( a, b, \) and \( c \).

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