
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 given by segments and curves as described:

- For $x \in [-3,0]$, the function is linear with $y = -2 - x$.
- For $x \in [0,2]$, the function follows the top half of a circle with center at $(2, -2)$, defined by $y = \sqrt{4 - (x-2)^2} - 2$.
- For $x \in [2,3]$, the function is linear with $y = 2(x - 2)$.

For constants $a$, $b$, and $c$, the function $h(x)$ is defined as:
\[ h(x) = 2f\left(\frac{x}{3}\right) - 6. \]
Identify the ordered triple $(a, b, c)$ for the function $h(x)$.

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