
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 described as follows:

1. $y = -2 - x$ for $-3 \leq x \leq 0$
2. $y = \sqrt{4 - (x - 2)^2} - 2$ for $0 \leq x \leq 2$
3. $y = 2(x - 2)$ for $2 \leq x \leq 3$

Given constants $a$, $b$, and $c$, the function $h(x)$ is defined by 
\[ h(x) = a f(bx) + c \]
The graph of $y = h(x)$ appears as the graph of $y = f(x)$, stretched horizontally by a factor of 3, shifted right by 2 units, and shifted up by 5 units.

Determine the ordered triple $(a,b,c)$.

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