
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
Consider the function \( g(x) \) defined by the piecewise rule:
\[ 
g(x) = 
\begin{cases} 
-x-3 & \text{if } -3 < x \leq 0  \\
x-3 & \text{if } 0 < x \leq 2 \\
x^2 - 4x + 6 & \text{if } 2 < x \leq 3
\end{cases}
\]
Graph the function \( y = g(x) \) and determine the coordinates of all critical points where the function has a local maximum or minimum.

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