
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 piecewise function \( f(x) \), where:
\[ f(x) = \begin{cases} 
-x-2 & \text{for } -3 \leq x \leq 0 \\
\sqrt{4 - (x - 2)^2} - 2 & \text{for } 0 < x \leq 2 \\
2(x - 2) & \text{for } 2 < x \leq 3 
\end{cases} \]
determine the graph of the function \( g(x) = -f(x) + 1 \).

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