
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
Given the graph of \(y = f(x)\) which consists of:
- A line segment from \((-3, 1)\) to \( (0, -2)\),
- A semicircle from \( (0, -2) \) to \( (2, -2) \),
- A linear part from \( (2, 0) \) to \( (3, 2) \).

Define a new function \( g(x) = 2f(2x - 1) - 3 \). Draw or describe what transformations are applied to \( f(x) \) to obtain the graph of \( y = g(x) \) and determine the ordered triple \( (a, b, c) \) in the general transformation formula \( g(x) = af(bx) + c \).

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