
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 $y = g(x)$ consists of three pieces:
- For $x \in [-4, -1]$, \( y = 3x + 2 \)
- For $x \in [-1, 3]$, \( y = -\sqrt{9 - (x - 1)^2} + 2 \)
- For $x \in [3, 5]$, \( y = -3(x - 3) + 1 \)

What would be the graph of the function $y = -2g(x) - 1$?

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