
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 function $y = h(x)$ described by the following segments:
- $y = -3 - x$ for $x \in [-4, 0]$,
- $y = \sqrt{9 - (x-3)^2} - 3$ for $x \in [0, 6]$,
- $y = 3(x - 3)$ for $x \in [3, 4]$.

For constants $p, q, r$, define a new function $k(x) = ph(qx) + r$. The graph of $y = k(x)$ is obtained by stretching $h(x)$ horizontally by a factor of 3 and shifting it down by 5 units. Determine the ordered triple $(p, q, r)$.

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